- Email: [email protected]
Scanning Low-Energy Electron Microscopy
ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL. 128
Scanning Low-Energy Electron Microscopy ILONA MULLEROV/i~ and LUDI~K FRANK Institute of Scientific Instruments AS CR, Krdtlovopolskdt 147, CZ-61264 Brno, Czech Republic
I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. M o t i v a t i o n s to L o w e r the E l e c t r o n E n e r g y . . . . . . . . . . . . . . . . . . . . . A. E x t e n s i o n s to C o n v e n t i o n a l M o d e s of O p e r a t i o n . . . . . . . . . . . . . . . B. N e w O p p o r t u n i t i e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Issues I n h e r e n t to Slow E l e c t r o n B e a m s . . . . . . . . . . . . . . . . . . . . III. I n t e r a c t i o n of Slow E l e c t r o n s w i t h Solids . . . . . . . . . . . . . . . . . . . . . . A. Elastic S c a t t e r i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. S c a t t e r i n g on N u c l e i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Reflection o n E n e r g y G a p s . . . . . . . . . . . . . . . . . . . . . . . . . . B. Inelastic S c a t t e r i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. S c a t t e r i n g o n E l e c t r o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Scattering o n A t o m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. P e n e t r a t i o n o f Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. H e a t i n g a n d D a m a g e of the S p e c i m e n . . . . . . . . . . . . . . . . . . . . . E. S p e c i m e n C h a r g i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. T o o l s for S i m u l a t i o n o f E l e c t r o n Scattering . . . . . . . . . . . . . . . . . . IV. E m i s s i o n o f E l e c t r o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. E l e c t r o n B a c k s c a t t e r i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. C r y s t a l l i n i t y Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. C o h e r e n c e w i t h i n the P r i m a r y B e a m S p o t . . . . . . . . . . . . . . . . . . . D. S e c o n d a r y E l e c t r o n E m i s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . V. F o r m a t i o n o f the P r i m a r y B e a m . . . . . . . . . . . . . . . . . . . . . . . . . . A. T h e S p o t Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. I n c o r p o r a t i o n o f the R e t a r d i n g Field . . . . . . . . . . . . . . . . . . . . . . C. T h e C a t h o d e L e n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. T h e Pixel Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. S p u r i o u s Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Testing the R e s o l u t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. D e t e c t i o n a n d S p e c i m e n - R e l a t e d Issues . . . . . . . . . . . . . . . . . . . . . . . A. D e t e c t i o n Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. D e t e c t o r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Signal C o m p o s i t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. S p e c i m e n Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. S p e c i m e n Tilt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
310 314 314 316 317 319 320 320 323 324 324 328 331 334 336 340 343 345 350 353 354 361 362 366 369 374 377 379 381 382 387 393 394 397
VII. I n s t r u m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A d a p t a t i o n o f C o n v e n t i o n a l S E M s . . . . . . . . . . . . . . . . . . . . . . . B. D e d i c a t e d E q u i p m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. A l i g n m e n t a n d O p e r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . .
399 399 401 407
309 Copyright 9 2003 Elsevier Inc. All rights reserved. 1076-5670/2003 $35.00
310
MULLEROVA AND FRANK
D. Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Selected Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Prospective Application Areas. . . . . . . . . . . . . . . . . . . . . . . . . . B. General Characteristics of Micrograph Series . . . . . . . . . . . . . . . . . C. Surface Relief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Critical Energy Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Diffraction Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Contrast of Crystal Orientation . . . . . . . . . . . . . . . . . . . . . . . . . G. Layered Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Material Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Electronic Contrast in Semiconductors . . . . . . . . . . . . . . . . . . . . . J. Energy-Band Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
410 413 414 415 417 418 419 422 422 425 426 430 431 432 432
I. INTRODUCTION Two versions of the electron microscope, the directly imaging (usually T E M , transmission electron microscope) and scanning (SEM) models, have coexisted in the instrument market and in laboratories for decades and none of them seems likely to lose ground. At certain periods, one or the other attracts enhanced attention and makes a more significant step forward, leaving afterwards the m o m e n t a r y leadership to the competing principle. A period rich in innovations has been experienced by SEM designers and brought two successful novelties, namely the environmental SEM with the specimen surrounded by a gas at a pressure of thousands of Pa and high-resolution imaging at electron beam energies down to fractions of eV. Our purpose here is to review the theoretical and practical aspects of the latter and to present the method as being already fully feasible and worth employing in the majority of SEM application areas. The term "low-energy" electron is obviously of a qualitative nature and should be given some quantitative limits. This limit could be best based on characteristics of the electron interaction with solids that provides the image signal in SEM. Examining the typical energy dependences of all relevant quantities connected with this interaction, we can find good reasons for the definition of two such energy intervals instead of only one. Figure 1 shows the atomic number dependence of the so-called second critical energy Ec2, i.e., the higher of two electron impact energies at which the total electron emission yield is equal to one (or to 100%). These energies exist for nearly all solids with a few exceptions such as conductors of lowest mean atomic numbers, for which the total emission does not exceed the unit level. Above Ec2 the electron emission decreases monotonically and no thresholds can be
SCANNING LEEM
311
6 O
Ec2 [keY] 4
O
. . . . . . . . . . . . . . . . . .
J .
_ .O . . . . . . . . . . . . . . . . . . . . . .
o
o
8
0
o
o~
o
oo q~
2
.............
o
O ....................
0
0 , ~
'0
0
~
0
o ~ 0
o ,
.............................................................
20
........
0
40 60 atomic number
, ......
,,,,,,,
.......
,~ . . . .
80
FIGURE 1. The higher of the critical energies for normal electron impact, Ec2, at which the total electron yield is equal to one, plotted versus the atomic number for conductive chemical elements; data were collected from Bauer and Seiler (1984) and Zadra~il and E1-Gomati (2002). identified. On the contrary, the energy Ec2 alone represents a significant breakpoint at which the specimen charging changes its sign. As the graph shows, a value like 5 keV can be taken as a margin of this interval. Thus, let us consider the "low-energy" range below 5 keV beam energy. As will be shown subsequently, around this threshold the yield of backscattered electrons (BSE) also loses its monotonic dependence on the atomic number, which exists at higher energies, so that the conventional material contrast ceases to be reliably usable. In Figure 2, the well-known plot of the inelastic mean free path (IMFP) of electrons is shown versus energy for numerous elements and compounds. The deep minimum at approximately 50 eV represents another crucial threshold: the I M F P starts to grow below this point because the main interaction phenomena, the secondary electron (SE) emission in particular, settle here and a fundamentally new situation emerges for the scanned imaging. So let us define also the "very low energy" interval below 50 eV. Later we will see that this energy range can be further subdivided but this would miss its practical purpose. The commercial SEM instruments traditionally used primary beam energies of 15-30 keV as a compromise between sufficiently small spot size and reasonable SE emission. The series of preadjusted beam energies in SEM mostly ended at 5 keV and when even lower energies were possible, good-quality micrographs were not acquired. Progress in the computeraided design methods for electron optics opened ways to tailoring the objective lenses and even full columns to desired parameters and afterwards the SEM instruments entered the low-energy range down to about 1 keV.
312
MLTLLEROYA AND FRANK '~
' I"'lli'illll
'i
i Ililili ....... '1 I I'11'11|1" I I iI~_
E - E,, (eV)
FIGURE 2. The energy dependence of the inelastic mean free path of electrons; the dots represent various elements and compounds. (Reprinted with permission from Seah and Dench, 1979.) The motivation included the suppressed charging and better visualization of surface relief details that projected itself, among others, into more precise measurement of distances in the images. This experience made the lowenergy range known and acceptable for the community of microscopists but no trends to push the energy further down have been apparent albeit possible sources of motivation existed for a long time in experimental areas adjacent to SEM. The so-called emission electron microscope (EEM) is in fact one of the oldest versions of EM. In this type of directly imaging microscope the specimen itself is the source of electrons, which are emitted under excitations that include impact of photons, electrons and/or ions or high-temperature heating. More than 60 years ago Recknagel (1941) published a theoretical study showing that the immersion objective lens, a crucial part of EEM that accelerates the electrons emitted at quite low energy E0 to some final energy E and forms the first image of the emitting surface, has surprisingly good properties. Its basic aberration coefficients are proportional to the ratio Eo/E so that they decrease even for the lowest emission energies. Of the EEM versions mentioned, the photoemission one (PEEM) is most often met in laboratories at present, partly because of the progress in this method, connected with extended availability of intensive radiation sources at synchrotrons. However, for us another version of the EEM is most important, namely the low-energy electron microscope (LEEM), in which the specimen excitation is made via a parallel coherent wave of slow
SCANNING LEEM
313
electrons. The method and instrument were first proposed by Bauer (1962) and demonstration experiments were later performed by Delong and Drahog (1971). Only in the 1980s did the first micrographs appear in the literature (Telieps and Bauer, 1985) but since then the method boomed; for a review see Bauer (1994), while more practical aspects are summarized by Veneklasen (1992). Although the LEEM apparatus remains an expensive tool for top specialists, it produced the most attractive and fruitful results from among the surface examination methods except, maybe, probe microscopies. The scanning LEEM (SLEEM) method described here aims at achieving similar results as regards observability of surface-localized physical phenomena, with possibilities of extension toward multiple signal detection. The idea of reversing the function of the immersion objective lens with respect to that in EEM can be originally found in Zworykin et al. (1942) where an electrostatic SEM with biased specimen is outlined. Adaptation to a conventional SEM, by inserting a retarding field element below its objective lens, was published by Paden and Nixon (1968). Yau et al. (1981) demonstrated lowering of the aberration coefficients by means of a retarding field, either overlapped over the focusing magnetic field or arranged sequentially, and even measured the aberration coefficients down to tens of gm at very low energies but their aim was solely to improve tools for electron lithography and annealing and they did not consider any application to scanned low-energy imaging. Many other attempts to retard the primary beam electrons before their impact onto the specimen were published and this history is reviewed by Mtillerovfi and Lenc (1992a). It is interesting that, although many of the previous studies proposed quite feasible solutions to the problem of decelerating the beam in SEM, none of the reviewed papers presented convincing results, i.e., micrographs collected throughout the full energy scale. To our knowledge, the first such series was published by us (Mtillerovfi and Frank, 1993) together with practical experience from adaptation of a commercial SEM to the SLEEM method. The low-energy microscopy program at ISI Brno was started in the 1960s (see above) and after a long break it continued with the first demonstration experiments with the SLEEM method (Mtillerovfi and Lenc, 1992b) and theoretical examination of properties of the immersion objective lens (IOL) (Lenc and Mfillerovfi, 1992a,b). The problem of IOL and its optimization was systematically treated by Rose and Preikszas (1992) and Preikszas and Rose (1995). More literature references will be given below. One could easily conclude that the method and Corresponding apparatus have been sufficiently explored to appear on the instrument market and to
314
MULLEROVA AND FRANK
enter the broad community of users. Moreover, the method may be launched after quite moderate adaptation to a conventional SEM. Nevertheless, the small number of existing instruments corresponds to only a handful of users, who do not represent a sufficient marketing target, so that the barrier has not been broken yet. The first commercial device is expected in 2003. In the following the SLEEM method will be discussed in detail from all fundamental viewpoints so that the reader can comprehend it and even start to use it. The scope of the application results is still quite limited and awaits additional users who could contribute to filling the obscure areas in the interpretation of the contrast observed.
II. MOTIVATIONS TO LOWER THE ELECTRON ENERGY The low-energy range below 5 keV is now available in commercial SEM instruments and widely used, for observation of nonconductors, for measurement of dimensions in images, for improved observation of surface relief, etc. In this chapter we will summarize the main advantages of working in this energy range and then continue with the very-lowenergy range. Let us mention here that practical experience with image contrast (and therefore also the awareness of motivation for using it) is quite naturally concentrated mainly in the energy ranges of commercial instruments. These mostly provide quality imaging down to 1 keV where the resolution value is often still guaranteed. Somewhere below 1 keV the imaging properties "break down" and the image quality becomes unacceptable--this threshold is usually met around 500 eV. For microscopes containing compound objective lenses, this limit is shifted to about 200 eV and the performance of devices equipped with an aberration corrector is similar.
A. Extensions to Conventional Modes of Operation 9 It is well known (and also evident from Figures 13 and 16) that the total electron yield a per incident electron, acquired from any known specimen, increases when the primary beam energy is reduced below its usual value of 15 to 30 keV. This is because of shrinkage of the interaction volume together with the path of generated secondary electrons towards the surface, which reduces absorption. Because a is generally less than 1 at high energies, its increase leads to a decrease in the portion of electrons dissipated in the specimen, suppression of
SCANNING LEEM
9 9
9
9
9
9
9
315
charging of nonconductive specimens, and lesser demands on requirements to make them conductive. At the critical energy Ec2 we get ~r= 1 and a true noncharging microscopy is possible (Frank and Mtillerov~t, 1994). As the SE yield 6 keeps growing even when below Ec2, a significant signal increase with respect to the traditional beam energies is achieved, which projects itself into improved signal-to-noise ratio (SNR) in the image. Measurements on elemental specimens showed that the SE signal maximum appears at energy Em between 100 and 800 eV (e.g., Seiler, 1983) and below this energy the yield again falls. The so-called material contrast, based on direct proportionality between the mean atomic number of the specimen and the yield 7/of backscattered electrons, which is reliably available at tens of keV, disappears in the low energy range in the sense that the r/(E) curves for various specimens start to cross each other (see Figure 13). Instead, for particular combinations of materials, optimum energies can be found at which the mutual contrast reaches its maximum (see Mfillerovfi, 2001). As the interaction volume of slower electrons diminishes, information generated in the microscope becomes better localized and more sensitive to the true surface, which is then also more truly visualized. Tiny protrusions and ridges appear on facets that were apparently smooth at higher beam energies. The so-called edge effect, i.e., overbrightening of steeply inclined facets or side walls of surface steps that is apparent and mostly dominant at tens of keV, diminishes here and fully disappears somewhere below 500 eV (in fact near Em for the maximum SE yield). The reason is that the penetration depth of primary electrons (PE) shortens and approaches the escape depth of SE. Consequently, all generated SE are emitted and no surface steps can extend the emitting area. Experience has shown that, in the range of hundreds of eV, a contrast between various grains appears on polycrystalline specimens. This phenomenon needs to be explored more carefully because in principle there are several possible explanations: in addition to dependence of both the generation and absorption of SE and of the electron backscattering on the crystal orientation, the presence of thin surface films can also play a role as these layers cease to be transparent here and their thickness (like that of oxides) is also orientation dependent. The energy dissipation in the specimen is clearly smaller at low energies--each electron delivers less energy. The increase in emission of slow SE makes no significant change and the BSE emission, which is responsible for the great majority of the energy export, is roughly
316
MOLLEROVA AND FRANK
constant down to hundreds of eV (see Figure 13). Nevertheless, at higher energies and still at 1 keV the penetration depth (or electron range) decreases faster than linearly (see B6ngeler et al., 1993) so that the spatial density of dissipated energy grows. Then this decrease gradually becomes linear (Joy and Joy, 1996) and the density of dissipated energy stays constant because the deficit in the energy income is just compensated with thinning of the interaction layer. 9 The question of radiation damage is even more complicated than the previous issue. In addition to changes in the total amount of dissipated energy and in its spatial density, the cross-sections for various inelastic phenomena also depend on the energy of incident electrons. For example, cracking of hydrocarbon molecules and creation of the contamination graphitic layer is most effective for electron impact at about 100 to 200 eV. Only in the very-low-energy range do the elastic collisions dominate and the radiation damage diminishes and disappears.
B. New Opportunities
9 In the very-low-energy range, the wavelength of incident electrons, )~ [nm]= 1.226 x {E[eV]} -1/2, becomes comparable with the interatomic distances. As in the classical LEED (low-energy electron diffraction) apparatus, the angular distribution of the reflected electrons is strongly anisotropic and the intensity is concentrated into diffracted beams. In our case, the incident wave is convergent and one can refer to the CBED (convergent beam electron diffraction) method used in the STEM (scanning transmission electron microscope). Selective detection of some diffracted beams enables one to directly visualize the surface crystallinity and its possible changes. 9 Flat clean crystal surfaces are composed of terraces that are smooth on the atomic level and separated by steps of a height of one or more atoms. If the primary spot illuminates a terrace margin and the electron wavelength is in suitable relation to the step height, the two parts of the wavefront, reflected on adjacent terraces, can interfere (the dividedwavefront interference) constructively or destructively and reveal the step although the point resolution of the microscope does not reach the atomic level. 9 A similar phenomenon can be observed when the interference concerns electrons reflected from upper and lower interfaces of a thin surface film (the divided-amplitude interference). At wedge-shaped layers,
SCANNING LEEM
9
9
9
9
317
equal-thickness stripes (an analogy to Newton's rings) should be observed. Electrons impacting the solid with energy just above the surface potential barrier are, according to laws of quantum mechanics, subject to partial reflection so that the height and shape of the barrier can be sensed. It is known from LEED experiments that the electron reflection (Bauer, 1994; Barto~ et al., 1996) is inversely proportional to the local density of electron states coupled to the incident wave. This phenomenon can appear only below 20 or 30 eV of landing energy. The contrast based on the local density of states enables one to directly observe the energy band structure, which opens ways to attractive applications, e.g., in development and diagnostics of semiconductor structures (Frank et al., 2002; Mfillerov~ et al., 2002). Already in the low-energy range (and especially for heavier specimens), the elastic electron scattering displays behavior that can be described solely by the quantum mechanical Mott cross-sections, which incorporate screening of the nucleus by electrons, existence of the spin, and the spin-orbital interaction (see, e.g., Reimer, 1998). Thus, the electron spin influences the image signal and the magnetic microstructure becomes observable provided a spin-polarized beam is used for the illumination (Bauer, 1994). As mentioned above, below about 20 to 30 eV elastic collisions of incident electrons start to dominate so that radiation damage becomes negligible. This can be important for examination of highly sensitive materials and also, for example, for interoperational checks in semiconductor production where any damage should be avoided.
C. Issues Inherent to Slow Electron Beams
Problems with the generation of sufficiently small electron probes in the lowenergy range have been solved reasonably satisfactorily and these beam energies are available in modern instruments. Nevertheless, the low-energy range has been explored only down to about 200 eV, as already noted. Let us now summarize the problems that have to be overcome when lowering the beam energy with an instrument having this energy constant throughout the microscope column. 9 The chromatic aberration of electron lenses depends on the ratio A E / E , where the energy spread AE within the beam is given by the emission mechanism used in the gun and E is the beam energy within the lens.
318
9
9
9
9
9
9
MOLLEROVAAND FRANK Obviously, the chromatic aberration disc enlarges with decreasing energy and in the low-energy range it usually dominates as regards the image resolution and affects this crucial characteristic adversely. The diffraction aberration, i.e., the size of the Airy disc arising from interference of the unscattered electron wave, passing through the aperture-restricting diaphragm, with the marginal wave scattered on the diaphragm edge, is proportional to the wavelength ~, i.e., to E -1/2. Thus, this contribution to the final spot size also grows at low energies. The electron current extracted from the gun is proportional to the extraction voltage. For thermionic cathodes, the gun brightness is linearly proportional to E (Reimer, 1998). For Schottky- and fieldemission guns, this proportionality is not so simple because the first acceleration voltage controls the emission and the final beam energy is adjusted afterwards. But the beam current always decreases with decreasing energy. In spite of some screening against the spurious electromagnetic fields coming from the environment, particularly the a.c. ones, which is secured by the material of magnetic circuits, some undesired influence is usually observed. This grows strongly at low energies and is proportional to the time of flight through the column, i.e., to E-1/2. The situation is most critical in the ultrahigh-vacuum (UHV) devices where the chamber walls are traditionally made of nonmagnetic materials. Any narrow directed beams of charged particles suffer from mutual interaction of those particles via Coulomb forces. Particularly in crossovers, the mutual repulsion intensifies so that the size of these crossovers becomes larger than that given by geometrical optics. The consequences of the inner interaction are strongly dependent on the beam current, and for low currents and Gaussian beam profile the crossover broadening is proportional to E -3/2 (Spehr, 1985). In connection with the previous point we should also mention that another consequence of the electron-electron interaction within the beam, and again mainly in crossovers, is broadening of the energy spread (so-called Boersch effect). Here again the situation depends on the beam current and also on the crossover shape and dimensions; for stigmatic focusing the mean quadratic broadening AE is proportional to E 1/4 (Rose and Spehr, 1980) so that figures are even slightly more favorable at low energies. The conventional detector of secondary electrons of the EverhartThornley (ET) type (Everhart and Thornley, 1960) relies upon extraction of SE by means of the front-grid bias to about 300 to 500 V and subsequent acceleration of them with the scintillator potential of
SCANNING LEEM
319
about 10 kV. These electrostatic fields, oriented laterally to the optic axis, might be found damaging to the primary beam geometry in the low-energy range. Thus, novel approaches to the detection strategy are needed. With decreasing electron energy and reduction of the active depth of signal generation, the surface cleanliness becomes more important. At energies near to the minimum of IMFP the penetration depth of PE becomes comparable with the thickness of contamination layers, both that of the graphitic carbon from cracked hydrocarbon molecules and that of oxide or other products of the surface reactivity. From this point of view, the vacuum conditions within the specimen chamber become more important, as in the case of electron spectroscopies. However, in the very-low-energy range the IMFP again extends and normal vacuum demands are restored. It is obvious from this list of issues that major obstacles arise from physical principles and can only be avoided by keeping the primary electron beam at high energy for as long as possible and decelerating it only shortly before its impact on the specimen. This approach has already been applied in various modifications that will be outlined here and completed with some new data and experience of the authors.
III. INTERACTION OF SLOW ELECTRONS WITH SOLIDS
The physics of electron scattering and diffusion in solids is described in many original papers and also good textbooks. Precise and sufficiently detailed analysis of the problem for nonspecialists can be found in the book of Reimer (1998) and a condensed review of the scattering phenomena suffered by very slow electrons has been published by Bauer (1994). In this chapter we summarize the main approaches only briefly and depict basic differences inherent to low- and very-low-energy ranges. Elastic scattering on atom nuclei and inelastic scattering connected with excitation of electrons belonging to the target are fundamental processes determining the range of incident electrons, in-depth distribution of the ionization processes, and consequently also emission of the secondary and backscattered electrons. In order to characterize the individual scattering processes, usually the quantity known as the differential cross-section d~/d~2 is used, which shows the relation between the distance of the original electron trajectory from the scatterer and the angle of its deflection 0, and represents the probability that an electron approaching the target will be scattered into a solid angle d~2.
320
MULLEROVA AND FRANK
Integrating over f2 we get the total cross-section cr. Multiple scattering is described via statistical quantities, first of all by the mean free path between collisions. Multiple elastic scattering causes broadening of the incident beam up to possible backscattering while multiple inelastic scattering causes gradual loss of the electron energy along its trajectory. For us, the most important inelastic process is release of a secondary electron.
A. Elastic Scattering 1. Scattering on Nuclei
Scattering of incident electrons on nuclei of the specimen atoms is considered elastic when the mass of the nucleus is regarded as so large with respect to the mass of the electron that after interaction the nucleus remains in rest. This simplifying assumption neglects generation of phonons, which becomes apparent particularly at the lowest electron energies where other losses already vanish. Nevertheless, we will mention this type of scattering among the inelastic types. In the frame of classical mechanics, we can solve the Newton equation containing the attractive Coulomb force between a positively charged nucleus and the negative charge of an electron. The result of the classical calculation of the differential cross-section, first published by Rutherford in 1911, is (for electron energies negligible with respect to the rest energy E 0 = me 2 = 511 keV) given by dcrez
e4 Z 2
1
dr2 = 16(4rce0)2E2 sin4(0/2)
(1)
where e and m are the electron charge and mass, respectively, e0 is the permittivity of vacuum, and Z is the atomic number of the nucleus. This relation is acceptable for electrons above 100 keV but at low energies it represents a bad approximation. It diverges at 0 = 0 because the small scattering angles arise for electrons flying far from the nucleus where in fact its potential is screened by electrons of the atom. At large scattering angles the approximation also fails owing to neglect of relativistic effects (Reimer, 1998). The screening effects can be described solely by quantum mechanics by determining the scattering amplitude f(O) of a spherical wave scattered on the atom and superposing it on the incident plane wave. The differential cross-section is then generally expressed as daez/dfa = If(O)l2.
(2)
SCANNING LEEM
321
The scattering amplitude for the screened Coulomb potential can be found by solving the Schr6dinger equation for ground states of the atom electrons. A good approximation is the exponential screening with the screening radius equal to R s - a i _ i Z -1/3, where a/4=0.0569 nm is the Bohr radius; this gives, after substitution into Equation (2), the so-called screened Rutherford cross-section dote1
e4 Z 2
1
dr2 = 16(4~e0)ZE 2 [sin2(0/2) + sin2(00/2)] 2
(3)
with 00 ----X/2TcRs (Reimer, 1998). This cross-section already produces finite values for small 0 and can be further improved by taking into account the full series of exponential potentials instead of only one, by incorporating potentials from neighboring atoms (e.g., via so-called muffin-tin model), by modification of the scattering potential by correlation and exchange phenomena between incident and target electrons, etc., and/or decomposition into partial waves can be used. The exact cross-sections, so-called Mott cross-sections (Mott and Massey, 1965), for elastic large-angle scattering may be obtained for the screened Coulomb potential when the relativistic Schr6dinger or PauliDirac equation is used. The result is then in the form of a superposition of terms belonging to both spin directions with respect to the direction of propagation but no analytical expression for da/df2 can be written. For an unpolarized electron beam, the Mott cross-section remains axially symmetric and in the general Equation (2) two formally identical members are summed on the right-hand side. These can be then developed into a series of Legendre functions (e.g., Ding and Shimizu, 1996). In addition to modified values at large scattering angles, the Mott cross-sections exhibit one property not met before, namely nonmonotonic angular dependence as shown in Figure 3. Obviously, this behavior emerges in the lowenergy range for large Z while for small Z it is not present until near the very-low-energy range. Data regarding the Mott cross-sections for chemical elements at low and even very low energies can be taken from numerous sources (see, e.g., Reimer and L6dding, 1984; Czyzewski et al., 1990; Werner, 1992). The role of the electron spin in scattering was examined by Kirschner (1984). When decreasing the energy of incident electrons toward the verylow-energy range, the Mott cross-sections, expressing a relativistic freeelectron scattering incorporating partial waves, overestimate the scattering rate and bring unrealistic short elastic mean free path (EMFP) in tenths of nm only. It was suggested (Fitting et al., 2001) that they should be
322
MOLLEROVA AND FRANK
10 "is
~;x" k ~
AI
Au
x
10 "17
V i \ kLg..~,0kev 10 "16
"" "
~I,,
~4[,...._.7.0
;.o2:7 10 "21 0
.
.30 .
.
60 . . . 90. . 120 scattering angle, 0
150 '
v 10"o - .
-180 '
keY
.
3'0.
.
.~o . =- " 9'0 ~2o scattering angle, 0
~,o
~8o
FIGURE3. Differential cross-sections for elastic scattering of electrons at various energies, calculated by decomposition into partial waves. (Reprinted with permission from Ichimura, 1980.)
replaced here with factors inherent to quasi-elastic scattering on acoustic phonons; this mechanism works down to the thermalization threshold of electrons at mean energy 3KT/2, i.e., a few tens of meV, and preserves E M F P in the nm range. Then the scattered electrons are considered as quasifree Bloch electrons within a dispersion relation of the conduction band of the target. Acoustic phonons have energies of a few meV only, but scattering on them is nearly isotropic so that they effectively influence any oriented stream of electrons and, for example, lower the electric conductivity. While the total elastic cross-section (Tel characterizes a single scattering event, the multiple scattering is described by the E M F P
)~el
--
1/Naet
(4)
where N is the number of atoms per unit volume. As Figure 4 shows, this quantity also exhibits nonmonotonic behavior starting from the low-energy range. We can conclude that, for slow electrons, anisotropy appears already in scattering on single atoms and resulting features then combine with a directional segregation owing to interference of partial waves from a lattice of scatterers. Further, the path length between the scattering phenomena generally shortens down to the lowest energies but in the very-low-energy range this dependence is far from being monotonic.
SCANNING ~
I
O
Z
~ /',,"_ .....
IZ
_ i0o
to'
-
J
---:--::
/,,"
..~,
....
i II ,.-.. . . . . Wt.; ," / ' .,,"........,.">;~,." z;.r I0 I= / .." ' :. . ~ / : . . ' " , , . . . . ~ . .,,;~"
/
9;,"~-'~;,5;I..:.~:-",,,.--.~.I",,;,c.,-
........
.
--:.;-:-..::::;::,-
I--~ ~ f-f.-
,,
o
.. . . " i B
I
C ..-...-...-..-
,..'.-'",.-;,""
Cu I-~~ .,:... p).<
323
102
.......... Ge
["
LEEM
......
]" i #~ ; ,,~...... 2 ,~.~"x_;: I,, 9 i.~.-~" ! 11111
io'
to'
I01
ENERGY (eV) FIGURE 4. Calculated energy dependence of elastic m e a n electrons. (Reprinted with permission from Ding, 1990.)
I
I01
!
,, iii!
I
! 1t
I1
10 3
ENERGY leVI free paths
(EMFP)
for
2. Reflection on Energy Gaps Even above the vacuum level, the energy band structure exists and the energy states E(k) are separated by forbidden gaps, particularly where the kvector touches the boundary of the Brillouin zone. If the incident electron hits the gap, it does not enter allowed states and should be reflected. Nevertheless, total reflection is not obtained because the electron can pass an inelastic collision and lose energy or it changes its wave-vector owing to scattering on a phonon or some crystal imperfection--in both cases a shift to the allowed states can occur. In the range of units of eV elastic reflection is strongly enhanced. Electron microscopists have never had any reason to take this phenomenon into account, as its appearance requires the electron impact to be far below the energy range available in the SEM. But those using the VLEED (very-low-energy electron diffraction) method know the energy band structure region existing on the intensity vs. energy (I-V) curve for the specularly reflected (00) spot below the threshold where the first nonspecular diffracted beam appears (Jaklevic and Davis, 1982). It is important to note that the incident electron wave has to couple to the energy states into which it is to penetrate. This means those Bloch states inside the specimen, the surface-parallel wave-vector component of which is equal to KII-4-g, where KII is the vector component of the incident electron and g is any surface reciprocal-lattice vector (Strocov and Starnberg, 1995); in other words, those Bloch states that have dominant Fourier components resembling the incident wave (the coupling bands). The local extremes on the energy dependence of reflectivity R(E) are first of all connected with critical points of the energy bands E(k) at which OE/Ok_Lexhibits sharp changes or is equal to zero at the band-gap edges. When mapping those
324
MOLLEROVA AND FRANK
critical points upon variation of K,, complete bands in the symmetry planes of the Brillouin zone can be compiled (see Strocov et al., 1996). A further crucial condition is low absorption of electrons, which is met below landing energies of 25 to 30 eV. Simulations show that any local R(E) features are washed out at even moderate absorption (appearing for the imaginary part of the crystal potential exceeding 1 eV) and that the model fits better the experimental data when the nonisotropic situation is considered with absorption reduced in directions along the surface (Barto~ et al., 1996). In addition to extremes of R(E) revealing the critical points at the coupling bands, oscillations might also appear as minor features. These are connected with surface resonances caused by interference between the specular beam and a nearly emerged nonspecular diffracted beam moving parallel to the surface, and can be used for mapping the surface potential barrier (Jaklevic and Davis, 1982). Figure 5 demonstrates the reflection anisotropy connected with its k vector dependence, which enables one to get contrast between different crystal orientations at suitable energies. Mapping of the local variations in the density of states at the energy of the electron impact, for example those connected with the local doping of semiconductor structures, is also potentially available. B. Inelastic Scattering The term inelastic scattering is usually used to describe an interaction between the incident electron and the atomic electrons in the target. More generally, this should include all phenomena at which the impinging electron changes its energy. 1. Scattering on Electrons The main mechanisms of interaction between electrons include: 9 9 9 9
quasifree electron-electron collisions (i.e., a Compton-like scattering), excitation of electrons within partially occupied energy bands, excitation of interband transitions, excitation of plasmons, i.e., energy quanta connected with the charge density waves of valence or conduction electrons, and 9 ionization of inner shells of the atoms.
These mechanisms exhibit not only various cross-sections, but also represent very different amounts of energy interchanged between colliding particles. Although inelastic scattering is often assumed to cause only energy decrease
325
SCANNING LEEM
1.0
. . . .
II
I
'
i"
il
0.0 0.6 I,,i,J I:K
O.t,,
0.2 ei | n
"....:
0
!
,.
,1
1
a
5
10 E(eV)
15
20
FIGURE 5. Reflection coefficient R(E) of the W(ll0) and W(100) surfaces for slow electrons. (Reprinted with permission from Bauer, 1994.)
but not trajectory deflection, some collisions can be associated with large scattering angles (like the Compton scattering). In spite of this, the relevant differential cross-section is often considered in the energy scale instead of in the angular one, namely as d a / d W, where W is the transferred energy. Energies transferred at ionization range from a few eV up to nearly 100 keV depending of the atomic number and electron shell involved. Excitation of plasmons and electron transitions cause energy losses not exceeding tens of eV but the loss due to the electron-electron collision can be up to 50% of the initial energy. If we neglect any binding forces acting upon the target electron at rest and consider the incident electron approaching with energy E, we can use classical mechanics to get the differential cross-section (Reimer, 1998) dain
dW
~e 4
1
(4~e0) 2 E W 2"
(5)
This relation is derived upon the assumption that the target electron stays at rest during the collision and only acquires momentum--this is not the case for slow electrons and hence for E ~ 0 (and also for central collisions) this cross-section diverges. But Equation (5) indicates that this type of scattering is more common at low energies, that small energy losses are
326
MOLLEROVA AND F R A N K
more probable, and, because the same approximation gives the scattering angle 0 as sin20 = W / E ,
(6)
small scattering angles are also more probable. If this simplified approach is upgraded, correcting terms due to indistinguishability of electrons and due to their spin are added to 1/W 2. These are of the same dimension (energy) -2 and combine E, W, and E0. Thus, the added terms also grow at low energies but for W<< E these corrected relations converge to Equation (5). An equation derived by Gryzinski (1965), which takes into account the binding of electrons in atoms, also converges to Equation (5) for low binding energies. In fact, the "continuum" of losses owing to scattering on quasifree electrons appears in the EELS (electron energy loss spectroscopy) spectra only in the range of hundreds of meV (Reimer, 1995). The inner shell ionization can be solved in the same way as the problem of screening of the nuclear potential, i.e., by using the Schr6dinger equation for the nucleus, one atomic electron, and one incident electron, which leads to Equation (3). Now, excited states of the target electron are incorporated too and the final result, the total cross-section, e.g., for ionization of the K shell, is (Reimer, 1998) roe4 O'K -- (4~:e0)2
z x b x In u E2
(7)
u
where z/r is the number of electrons in the shell (z/r= 2), b/r is a constant factor (b/r = 0.35), E/r is the ionization energy of the shell, and u = E/E/r is the overvoltage. A maximum of a/r appears at u ,~ 3 for all atomic numbers and at lower energies a/r steeply falls. This means that throughout the lowenergy range the electron impact ionization is possible for every atom but in the very-low-energy range this type of scattering does not take place. The differential cross-section from the same calculation is
[(
dain _ e4Z as2 - (4rce0)ZE2 1 -
1 1 + (02 + 02)/02
)21
1 (02 + 62) 2
(8)
where the characteristic angle is OF_,--J/4E with J being the mean ionization potential of the atom (J [eV] ~ 10Z) and 00 is that from Equation (3). This relation is similar to Equation (3) and we can compare two characteristic features. First, at E = 5 keV the inelastic scattering is still confined to smaller deflection angles (e.g., for Z = 30, 00 is 10 times larger than 0E) but this
SCANNING LEEM
327
difference is less marked at lower energies. Second, the ratio of both differential and total cross-sections for inelastic with respect to elastic scattering is proportional to 1/Z, at least for large scattering angles. Within so-called dielectric theory, considering the solid described by the complex dielectric constant e and employing the analogy between the inelastic scattering of electrons and spatial attenuation of electromagnetic waves being proportional to the imaginary dissipative part of e, the differential cross-section can be written as (e.g., B6ngeler et al., 1993) d2tYin 1 Im[1 ] 1 d W d--------~- Tc2 aH----------~ e(W, 0) 02 + 02
(9)
with OD= W/2E. The analogy is based on modeling groups of electrons, similarly strongly bound within the given energy-band structure, by oscillators defined by their strengths and characteristic frequencies. So the problem is now shifted to determination of the complex dielectric constant e. Similar relations and results as regards the inelastic cross-sections are obtained when using the formalism characterizing the incident electron as a quasiparticle with self-energy, the imaginary part of which describes the quasiparticle lifetime while the real part expresses the shifts in the energy eigenvalues with respect to the noninteracting system. The same holds for the formalism of the electron-jellium correlation potential with the imaginary part governing attenuation of the dielectric response of jellium to the electron impact. Equation (9) used to be written also in variables W and q (the momentum) or q and w (with W = hw/2Tc). An overview of these approaches was published by Nieminen (1988). The energy loss function, written as Im[-1/e(q, co)], can be calculated on the basis of EELS experimental data for q = 0 (the "optical" data) when employing, for example, the quadratic dispersion relation (Kuhr and Fitting, 1999) ~o(q) -
~o(o) + ~
h
q2
.
(10)
Figure 6 shows an example of the measured dielectric loss function for SiO2 (Fitting et al., 2001). This contains peaks inherent in scattering on optical phonons, which will be mentioned in the next section. Calculations of quantities characterizing the inelastic scattering, which employed the dielectric function, were performed by many authors (e.g., Cailler et al., 1981; Powell, 1974, 1984, 1985; Penn, 1987; Egerton, 1986; Ding and Shimizu, 1996).
328
MULLEROV,~tAND FRANK
0
0.01
0.1
1 10 energy loss (eV)
100
1000
FIGURE6. The dielectric loss function for SiO2. (Reprinted with permission from Fitting et al., 2001.)
In Figure 7 we see the calculated energy dependences of ain for two elements, including the main contributions to crin. These curves reflect the general IMFP curve in Figure 2, which we used for the definition of the very-low-energy range (with IMFP, )~i,, defined analogously to Equation (4)). Further data regarding the IMFP behavior at low energies can be found in the work of Ding and Shimizu (1996), Powell (1987), Tanuma et al. (1991a,b), and others. We can notice that, starting from lowest energies, first the electron-electron scattering appears, then the ionization, and finally the plasmon excitation emerges. Let us repeat that the steep drop in crgnbelow about 50 eV is the most important feature here and also the reason for considering the use of this range as a separate mode of SEM. 2. S c a t t e r i n g on A t o m s
In the dielectric loss function in Figure 6, noticeable peaks that appear around 100 meV belong to scattering of electrons on optical phonons. Having formally separated the inelastic phenomena due to scattering on electrons in the previous paragraph, we discuss this mechanism here. The electron-phonon interactions are important mainly in dielectrics and insulators, but also in semiconductors. The forward scattering on longitudinal optical phonons (LO) is strongest. In 1969 Llacer and Garwin calculated (by means of Monte Carlo simulations) the secondary electron transport in alkali halides below 7.5 eV using the time-dependent perturbation of plane waves with the interaction Hamiltonian containing the polarization field caused by relative displacement of ions in the LO vibrational modes. Schreiber and Fitting (2002) discussed these phenomena in detail for SiO2 and included two LO modes with energies
SCANNING
LEEM
CTin[Cm 2]
329
o AI
1 0 "15
1 0 "15 I
1 0 "16
1 0 "16
; I
,i
\
-,~ \
"'... ".. " . \
" . . "-..",,
I..'
"
II 10"1'
1 0 "17
1
10
1 O0
1000 E[eV]
i
i . i Iil .
1
10
. .. . .
100
.
.
'\. .
"'~
"\-,,
1000 E[eV]
FIGURE 7. Calculated total inelastic cross-sections ( ) and their main contributions, namely the electron-electron scattering ( - - . - - . ) , shell ionization (. . . . . . ), and plasmon excitation (. . . . . . ). (Reprinted with permission from Ho et al., 1991.)
of 60 and 150 meV and also scattering phenomena representing both emission and annihilation of phonons. They also presented the scattering rates of collisions, which are much higher for the phonon emission phenomena. At about triple phonon energies, these rates reach their maxima between 1014 and 1015 s -] and toward higher energies they fall approximately as E -]/3. Thus, this scattering mechanism concerns mostly electrons with energy around 1 eV. It seems clear that, even when incorporating the phonon scattering, the enlargement of IMFP in the very-low-energy range (see Figure 2) is preserved at least for conductors and possibly for semiconductors. In Figure 8, comparison is made on the basis of data simulated by the Monte Carlo (MC) program employing the dielectric loss function (Kuhr and Fitting, 1999). Further, Figure 9 details the contributions to IMFP for SiO2, again presenting results of a MC program specialized to the very-low-energy scattering in semiconductors and wide-gap insulators. In addition to the mean free paths, both figures also contain the attenuation lengths characterizing a no-loss escape of electrons. We note that the energy range below 50 eV still has some structure in Figure 9, which could be utilized for the subdivision of this range. Nevertheless, this would be specimen-specific and would not allow any general conclusions to be drawn. In studies of the very-low-energy electron scattering, one more scattering mechanism is mentioned, namely the intervalley scattering (e.g., Schreiber and Fitting, 2002). This consists of collisions with suitable optical phonons, at which, in addition to energy loss corresponding to the phonon energy, additional energy and also momentum is transferred because the final state is in a different band or "valley" within a multiple-band structure. For SiO2, this type of scattering occurs much less frequently than the LO scattering.
330
MULLEROV,~ AND FRANK
i iimmk 10 l i i....... -"! I llllll--__tinel. i
mllmlll
m I'l'/
II!
l *,[ X',',',', I*, ........... ill,
-I
A~
Ii
i lllllll
n ,-,u II llilIHi I lllliil I IIIIIIII
Illl IWll
'"))11 I lllllll I I IIIIlil kr i [Ill !,[11,1, I,,,,,[[, ~'lll
[n~m]
IIImlll
,k ........
j ~ ,. ,
Illlllllll
I!i111111 , SI I I |1111111 . J lllllll
1 llllllll
il',lmm',mm[)~I[ II1111
igll
I!!!!! !
yllt
nel. ~111 ....
![ILLIILI/llL!'l![L!II ,,
l'kl.lllll ,I~I#IIHIII
IIIIIII 9 9
I i lilill/l:,l't iiliil
~
IIIIH
I lillllll I
a~o,.,. ~Itll~'llliiilll ill l lllltlll l"?lliiU
0.1
I,Im IIIIIIII Ir IIIIIIII IIIIIIIII I 'i
" IIIIIII IIIKi'llll J/IIIU]III I I1UUII IIlilV, t i
!
~;~ii:,i < ~,I,
i i ilmml'rl
,,,,,,'" i :, I IIIIIII
II
m,.7,,,,.,2 II ! l llml " !!!!!!!! !11111111 i,~
I l ltlllll 1 ~IIIIIII
nii~l][] IIIIIII ,ll[llli,lll
/II1[111~ IIIIIIII111111111/,7111
......
i iiiiiii
,I , , I,I,I I I U I. . . . . . . . . . .II. O | i l ~
ilUllii IIIIIII
I
l llllll
I
III
I Wl, i l l l l l
]
i
il
i iiii!!!,iiiiill i liillli
I J
I~llilll~
il'Ill~ I IIlillll
ii
I i liliiK k I I K~'fllllk Idlll~dl
~ltlmll
i lU~ a~n., ~ill I IIIUIII !
]iiiii]ii;i'hl1111111 II Llll ]llllil,i',II1111iiiiiii III]! Illllllll ,,,,,,, IIillllll 1
10
100
1000
1
10
100
1000
10
1
100
1000 E [eV]
FIGURE8. Elastic (el.) and inelastic (inel.) mean free paths and attenuation lengths (atten.) for Ag, Si, and SIO2, calculated by means of a MC program incorporating the Mott crosssections and the dielectric loss function. (Reprinted with permission from Fitting et al., 2001.)
numB
mmll
lie m~.n
m
mmm
~m|
-_-~
:i
i
m
m m m
III !111 0.01
.~ 0.1
1 energy
10 E (eV)
100
_ 1000
FIGURE 9. The mean free paths in SiO2 as a function of the electron energy for scattering at optical phonons (LO) and acoustic phonons (ac) and for impact ionization (ii), together with the attenuation length (at) for monoenergetic electrons. (Reprinted with permission from
Schreiber and Fitting, 2002.) For completeness we should also mention here the inelastic scattering of electrons on the screened Coulomb potential of the nucleus, leading to generation of an X-ray photon of the continuous emission (Bremsstrahlung emission). The low probability of radiative scattering on the nucleus can be demonstrated by comparing the ratio of the mean energy loss per unit trajectory Sraa to the analogous quantity for the electron-electron scattering. When using an approximate stopping power Se_ e according
SCANNING LEEM
331
to the Thomson-Whiddington law (see next section), we get the ratio (Feldman and Mayer, 1986)
Sraa4
Z (V) 2 Se-e -- 3r~ 137 c
(11)
which can be simply written as (Z/161) E/Eo so that in the low-energy range it falls to a value of the order of 10-3 or 10-4.
C. Penetration of Electrons The primary beam in SEM strikes the specimen surface at a point, the coordinates of which within the field of view are then used to describe the localization of all information collected during the dwell time of the beam. Nevertheless, the primary electrons penetrate to nonnegligible distances in all directions from the impact point and within this interaction volume they cause scattering phenomena and generate signal species. Thus, the abovedescribed single-scattering mechanisms are important not only for interpretation of the observed properties of emissions but also for tracing the spatial distribution of the information sources. The analysis of the electron penetration goes through the concept of multiple scattering, which can be characterized by statistical quantities only. We have mentioned the mean free paths for individual types of scattering. From Figures 2 and 4 or from Figure 8 it is obvious that, throughout the low-energy range, the ratio of rates for elastic and inelastic scattering is approximately constant and dependent on the mean atomic number of the target. The very-low-energy range is characterized by the onset of a strong dominance of the elastic scattering. When penetrating into the specimen (and, after undergoing some highangle scattering events, also into lateral directions) by a distance dx, the electron encounters N dx atoms (where N = NAp/A is the number of atoms per unit volume, Na is the Avogadro number, p the target density, and A the atomic mass). Thus, the decrease in the stream of unscattered electrons within the trajectory section dz is dI/I=-aNdz, where a is the total crosssection of one atom for a particular scattering mechanism. The unscattered intensity after passing the thickness l is I = I0 exp(-//)~) (with)~ as the mean free path), p=l/)~ is the mean number of collisions in the layer, and Pn =p'e-P/n! is the probability of n collisions for one electron. This simple model can be used only up to about p ~ 25 (see Reimer, 1998), i.e., only for tracing the penetration to distances of the order of 101 nm.
332
MI21LLEROVA A N D F R A N K
In the course of its penetration, the electron beam broadens as regards both its spread of angles and also its cross-section. Within the approximation of small energy losses and small scattering angles, the rootmean-square (RMS) width of the beam increases as l3/2 (Reimer, 1998). Nevertheless, this approximation is not good for low energies and successful modeling of the geometry of electron penetration is possible only by using tools such as MC programs. The multiple inelastic scattering is responsible for the finite length of the electron path within the target. The appropriate statistical quantity for the examination of this process is the stopping power S = dEm/dx (with dEm for the mean energy loss), corresponding to the continuous slowing-down approximation. This approach, which neglects discreteness of the collisions, does not allow study of the emission of elastically backscattered electrons (eBSE) but is useful for MC programs simulating the SEM image signals. When taking into consideration the e-e interactions only, the so-called Bethe formula, usually written as (Reimer, 1998)
2Tce4pZ NA ln(1 1 6 6 j )
(12)
S - (4~e0)ZE A represents the first approximation. For composite targets, the individual stopping powers have to be accumulated so that the relation for S contains a sum of terms like cm(zi/Ai)ln(bE/Ji), where C m are the mass fractions. This sum is often replaced by some energy-independent factor and the resulting expression is then called the Thomson-Whiddington law. Another practically convenient form of the stopping power relation for elemental targets is (Joy and Luo, 1989) S-
IoZ
-7850 ~
Zi
E
Z . ~- In ~//
[eV/nm]
(13)
l
where p is in g cm -3, Z i is the occupancy of the level i, and El. its binding energy. Equation (13) is claimed to work down to the binding energy of the outermost occupied level. While the differential cross-sections for the main scattering mechanisms are all proportional to E -z, the stopping power according to Equations (12) and (13) increases only as E -1. The validity of approximation (12) is restricted to high energies, notably in the dependence on the ratio E/J, so that for light elements it is acceptable down to about 1 keV. For lower energies, the correction J--+ J' = J/(1 + k J/E) with k TM 0.8 is possible. Below E/J 6.3 the energy dependence of S used to be replaced by S (x E -~ (Rao-Sahib and Wittry, 1974) but some authors assert that this parabolic =
SCANNING LEEM
333
relation overestimates the energy loss of slow electrons (see Ding and Shimizu, 1996). In the very-low-energy range, the stopping power seems to behave according to the statistical theory of Tung et al. (1979), in which electrons in the target are considered to form a homogeneous electron gas. Then S cxE s/2 for all targets (Tung et al., 1979; Nieminen, 1988), which corresponds to the sharp fall obvious in Figure 7. A theoretical model exists also for the most probable electron energy after passing a layer of the target, together with the distribution around this mean value. For SEM applications, the energy distribution of the backscattered electrons, which is mentioned below, is relevant. From the practical point of view, we need to know to what depth the primary electrons penetrate and what is the escape depth of the signal species. Various quantities have been defined to measure these distances and one of them is the attenuation length shown in Figures 8 and 9. The most useful is the electron range R, which can be defined in several different ways according to the method of measurement (see Reimer, 1998). Determination of the electron range is possible via measurement of the number of electrons T(x) passing a foil of a given material with some known thickness x. Because R depends also on energy E, it is convenient to use one foil thickness and to vary the energy. It is also advantageous to use an extrapolated value Rx (obtained by extrapolating the linear part of T(x) toward T = 0) instead of measuring down to really negligible transmission in order to get s o m e Rmax. Most of the experimental data obey a simple law R=aE n
(14)
with a around 10 and n decreasing from 5/3 at high energies to about 4/3 at low energies (B6ngeler et al., 1993). This relation seems to be valid down to about 1 keV and only few data exist below this energy. Salehi and Flinn (1981) verified the power law (14) for the penetration depth using two different amorphous glasses within the energy range 100 to 5000 eV and found n as 1.4 and 1.5 with the larger value for higher mean atomic number. The theoretical limit for the electron range can be obtained by integrating the stopping power S up to the particle "stop," which gives some Rs. Experimental data will provide lower values. According to Reimer (1998), for light elements with Z below about 20 we get Rmax ~ Rs and Rx ~=0.75Rs, while for high Z above 50, Rmax < Rs and Rx ~- 0.4Rs. Below 1 keV the electron range Rs exhibits a smaller slope of descent with decreasing energy than the data obtained by measurement of T(x) (Joy and Joy, 1996). Also the MC simulated electron range, as demonstrated by Kuhr and Fitting (1999) for Si and Au, has the slope decreasing below 1 keV
334
MOLLEROVA AND FRANK
toward a nearly energy-independent behavior at 100 eV, with values of 10 nm for Si and 6 nm for Au. One further parameter of the electron beam penetration is the depth distribution of the energy dissipation. The interaction volumes of the beam are roughly the same size for all specimens when distances are measured in the mass thickness px. Nevertheless, as the MC simulations show, for light elements the majority of scattering events is concentrated in the central level of the volume and somewhat below it while for heavy elements more scattering takes place above the central level.
D. Heating and Damage of the Specimen In introductions to papers dealing with low-energy microscopy, especially those concerning the instrumentation, we often meet formulations stating that the low energies are advantageous because of reduction in the specimen radiation damage. However, this opinion is wrong in most instances, at least within the low-energy range usually meant in the statements cited. Although the slow electrons really deliver less energy per impact, their interaction volume shrinks strongly and the spatial density of energy dissipation even increases. If the primary beam spot is considered stationary and its interaction volume hemispherical of a radius R/2, the temperature increase in the illuminated point amounts to (Reimer, 1998) AT
-
3dUI 2~cR
~
(15)
where U and I are the accelerating voltage and beam current, respectively, d is the portion of the incoming power that is dissipated into the specimen, and c [Js-lm-lK -1] is the thermal conductivity of the target. Obviously, the heating is proportional to E/R and because of Equation (14) AT increases at low energies. This heating is naturally higher for any noncompact material; e.g., for fibers it increases roughly in the ratio of their length to diameter (Reimer, 1998), and cannot be significantly suppressed by surface metalizing because of insufficient cross-section of the metal layer. When considering the electron probe scanning an island of area SA of a layer of thickness l >_R/2 from a low thermal conductivity (e.g., organic) material deposited onto a metal surface, we can derive the simple relation for its heating
A T -- djU ( l - R/4) c
(16)
SCANNING LEEM
335
with the illumination current density j = I/SA. Now we get AT decreasing at low energies but when SA denotes the size of the field of view on a larger area of this organic material, the lateral heat escape can reverse again the energy dependence of the heating, according to the relation between SA and R 2. In the low-energy range, the energies of emitted SE and BSE are still so different that in spite of the SE yield 8 being higher than that of BSE, r/, the energy output mediated by SE can be neglected. Thus, d ~ 1-rl and it remains nearly constant over the low-energy range. Further, because of 8 e~ E -~ (Drescher et al., 1970) at energies sufficiently above the maximum of 8, i.e., above, say, 2 keV (see the next section), we can operate with the primary current decreasing in the same ratio with the decreasing energy. Taking this into account, we find (even in Equation (15)) that the specimen heating slowly decreases at low energies down to about 2 keV where the increase starts again. The temperature distribution around the moving electron probe was studied by Kohl et al. (1981). For common materials, particularly metals, semiconductors, and even insulators with sufficient thermal conductivity, the temperature increase remains far below 1 K. Nevertheless, some materials such as foams and gels have very low thermal conductivity and their heating might be critical. These specimens were studied by, for example, Brown and Swift (1974), Berry (1988) and Price and McCarthy (1988). Mostly low-energy modes are recommended for sensitive specimens. The direct radiation damage of the specimen material consists first of all in breaking the chemical bonds, decomposition of molecules, and possibly release of gaseous components. Because it is generally ionization phenomena that are in question here, the energy dependence can be assessed according to the stopping power S. According to Equation (12), S cxln(E/J)/E, i.e., approximately S cx E -~ This is an even steeper slope than that of E -1/3, which results from the simplest assumption about the beam energy tlE/e (with t being time) distributed homogeneously into the depth measured by R cx E 4/3. Hence the spatial density of the radiation damage events increases throughout the low-energy range. For organic molecules the radiation damage mechanisms are diverse and it is not possible to survey them here. Let us briefly mention semiconductors. Incident electrons generate, for example in silicon, electron-hole pairs and holes can be trapped in the SiO2 layer where they have much lower mobility than electrons. Hence the density of surface states on the SiO2-Si interface increases, which in turn increases the rate of surface recombinations and the generated space charge might even cause layer inversion. For example, in MOS (metal-oxide-semiconductor) structures, the electron bombardment can induce changes in the threshold
336
MULLEROVA AND FRANK
voltage, gain, and dark current, i.e., in all the important parameters of the device. Some of these effects disappear only after long heating to temperatures above 250~ Nevertheless, significant suppression of these influences has been proved for electron energies below 1 keV, which are also used in IC (integrated circuit) testers. A special kind of radiation damage consists in breaking the carbon bonds to oxygen, hydrogen, and other atoms in hydrocarbon molecules. Owing to their high sticking coefficients, these molecules are always present on the inner walls of vacuum vessels including the specimen surface, unless this has been prepared or cleaned in situ. The carbon atoms then close double bonds and create a "polymerized" graphitic layer, the thickness of which progressively grows owing to easy diffusion of additional hydrocarbon molecules from the nonilluminated neighborhood of the field of view. Consequently, dark rectangles with darker frames indicate the areas of previous observation; these effects were studied by, for example, Fourie (1976, 1979, 1981) and Reimer and Wfichter (1978). At low current densities, the contamination thickness is proportional to dissipated energy, i.e., to the stopping power (which increases down to the boundary of the very-low-energy range). When all the molecules that have diffused into the illuminated area within a time interval are cracked in that time, the contamination rate saturates and then the contaminant accumulation becomes linear in time. As indicated above, the carbon contamination rate increases with decreasing E; according to experience, the situation around 100 to 200 eV is the most critical. Let us underline that, within a certain energy range of a few hundreds of eV, this phenomenon is the main obstacle against routine taking of micrographs (see, e.g., Figure 65). Fortunately, from the beginning of the very-low-energy range, this trend is reversed, elastic phenomena start to dominate, and the radiation damage disappears.
E. Specimen Charging
As already mentioned above, one important reason for using low energies in SEM is to gain an advantage in the perpetual fight of SEM microscopists against specimen charging (see, e.g., Pfefferkorn et al., 1972; Welter and McKee, 1972; Morin et al., 1976). In the next section we will see in more detail that in general the amount of charge emitted from the specimen differs significantly from the incoming charge. The difference is dissipated in the target and when this has a low conductivity, the absorbed current is not carried away from the illuminated area efficiently enough and significant charge density gradients arise. Furthermore, except for glasses and other
SCANNING L E E M
337
(5"m
,,,~e {.r G~~']
l
j
i
I ~ I
I I
I I
I I II eUs>O i r 1 I I
I l i I
I I leUs
I
|
I
I
....
Ecl
-'~,,
_a_~us'
E
l
I I
E Ec2 E
II,
I
E
Ep
FIGURE 10. Typical energy dependence of the total electron emission cr for specimen tilt angles 4)s > 4)2 > 4)] indicating the development of charging processes (see text for details).
homogeneous materials, the nonconductors and particularly specimens from the area of the life sciences are as a rule of a heterogeneous and anisotropic nature. Thus, the specimen charging is usually also inhomogeneous with the result that electric fields that vary strongly both in space and time are created above the surface. These fields destroy the micrograph geometry by deflecting and defocusing the primary beam, and also affect the brightness distribution by influencing the signal electron trajectories toward the detector. Qualitatively the issue can be comprehended from Figure 10. For every specimen, the total electron yield, a = 6 + 7, exhibits a maximum, which for the great majority of elements and compounds and for all nonconductors exceeds the value 1.0. When progressing from the conventional SEM energies around 15 keV downwards, the a(E) curve rises and crosses the unit level at the critical energy Ec2. This is the optimum energy for no charging and we will discuss ways of employing it for practical microscopy in Section VIII. Further, a(E) reaches its maximum at some Em' that more or less coincides with the maximum of the SE emission at Em (see the next section) and then descends, crosses again the unit level at Ecl and enters the range where no general curve can be drawn owing to very diverse behavior of the BSE emission. Finally, a(E)--+ 1 when approaching the mirror microscopy range at and below the zero energy impact. The differences in curves labeled with angles (~i express the angular dependence of the emission, which here means the influence of the specimen tilt and also of local inclinations corresponding to the surface relief.
338
MULLEROV~i AND FRANK
Suppose now the primary beam incident at energy E~>Ec2 o n a poorly conducting surface that exhibits a finite leakage resistance Ra between the illuminated point and ground; this is a measure of the ability of the specimen to carry the incoming charge away. We can characterize it by a straight line of slope ( e R J p ) -1 with /t, as the specimen current, which corresponds to a positive surface potential formed on Re. The potential drop across RG partially compensates the negative potential of the accumulated surface charge. The residual local potential decelerates the incoming beam so that its landing energy decreases causing a(E) to increase. This iteration continues until an equilibrium is reached at the point A for the final landing energy E where the incident and leakage currents are equal, leaving some net surface potential Us
S C A N N I N G LEEM
339
some negative charge again. The above-surface field is then dependent on the total charge distribution. Furthermore, the a ( E ) curve cannot be understood as a static property of the specimen since it exhibits a dynamical behavior, the specimen emission yields being affected by the penetrating charged species. We now look at the dynamics of the charging process based on our phenomenological model--these data will be needed for one important SLEEM application described below. F r o m the a ( E ) curve in Figure 10, we easily deduce E- E l a(E) - 1 =- ~ . (17) eRa Ip
Let us assume for simplicity that the charging process is characterized by only one time constant rc so that the accumulated charge develops as Q = Q m a x [ 1 - e x p ( - t / r c ) ] . This time constant will now be determined:
Qmax (18)
rc = (dQ/dt)t=o .
We consider the charged field of view to be a thin circular disc of diameter a and charge density q, situated in a medium of permittivity e. From the Coulomb law and the principle of superposition, we get the disc potential as Us = qa/2e. Figure 10 gives e Us = E - E', so that Qmax ~ qa 2 = 2 e a U s =
2Ea 8
(E - E').
(19)
At t = 0 the dissipated part of the beam current is [or ( E ' ) - 1] I p = d Q ( O ) / d t (< 0 for negative charging). In this equality, we substitute for a(E') the first two terms of the Taylor expansion around E and then substitute for a ( E ) from Equation (17). Finally we obtain
I]
{1
dQ
~ ( E - E') ~ - / t ,
~
.
(20)
t--0
The behavior of a ( E ) for energies above the critical energy can be estimated, according to the relations 17~ const and 6 cx E -~ (Reimer et al., 1992), as a ( E ) ~ - r l + ( 1 - o ) ( E / E c 2 ) - ~ which enables us to take the derivative in Equation (20). Substituting now from Equations (19) and (20) into Equation (18), we find for large RG the final result eaEc2
rc "~ 2.5 eli,(1 - r/)"
(21)
340
MULLEROVA AND FRANK
In order to get some quantitative figure, let us use the values rl=0.2, e r = 4 , Ec2 = 2000 eV, I e = 1 nA as an example. Then the time constant rc varies between 200 gs and 20 ms as the size of the field of view changes from 1 to 100 gm. Practical experience confirms that some charging is nearly instantaneous and might correspond to this range of rc but afterwards further changes in the image are usually seen for seconds or even longer. We stress that the above calculation differs from the approach often met in the literature (see, e.g., Shaffner and Van Veld, 1971; Welter and McKee, 1972; Cazaux, 1986), which considers the charging dynamics to be identical with the charging of a plate capacitor situated between the specimen surface and a metallic holder; then r c - p e . At high resistivity p, this time constant can be very long, e.g., about 3300 s for SiO2. Nevertheless, we recall that we aimed at getting a time constant for the progress in image destruction effects caused by the above-surface field, but the capacitor field is entirely closed between its plates and hence restricted to inside the specimen. A weak point of our approach is that the specimen current is considered to be of an ohmic nature, which might not always be realistic (see Cazaux et al., 1991). The crucial quantity in the above considerations is the critical energy Ec2. This quantity can be easily measured on conductors (via the absorbed current) but the opposite holds for the nonconductors that are of interest here; Reimer et al. (1992) summarized possible methods for this case. While in Figure 1 we have the values of Ec2 for some conductors, Joy (1989) published values for a choice of technologically important inorganic insulators between 550 and 3000 eV and for a selection of polymers, he found Ec2 from 0.4 to 1.8 keV. The 4~ dependence of Ec2, governing the scatter of these properties at rough specimens, can be estimated as Ec2(~b)= E c 2 ( 0 ) sec 2 ~b (e.g., Joy, 1989). This relation suggests that Ecz(60~ but detailed studies showed a less steep angular dependence and this ratio was found to be only around 2 and even smaller for insulators (Reimer et al., 1992). In particular, the angular dependence of Ec2 should weaken in the low-energy range together with the same trend regarding 3.
F. Tools for Simulation of Electron Scattering Phenomena connected with electron scattering inside the target, particularly in the case of multiple scattering met in SEM, are too complex for it to be possible to solve the "direct task," i.e., to reconstruct
SCANNING LEEM
341
the specimen from the SEM image or an image series, as can be done in certain circumstances in the TEM. Thus, efforts were oriented toward simulating the image of a fictitious specimen described by its scattering cross-sections. Two main approaches can be found in the literature: the transport equation approach and the Monte Carlo procedure. The transport equation is the equation for the phase-space density of electrons, n(r, ~, t), dependent on the position vector r, velocity vector v, and time t. All scattering phenomena that influence local values of n(r, v, t), including the generation of the incident beam, can be expressed by integrals containing the corresponding probabilities for movement within phase space (e.g., a (v--+ ~') for both inelastic and elastic scattering, differing by whether Iv[ = [u'l or not) and taken over the rest of the phase space. If a stationary case is considered, the terms increasing and decreasing the local density n compensate mutually, composing some integral equation for n(r, ~). In order to render the equation solvable, some simplifying assumptions are usually made, such as restriction to semi-infinite, amorphous, and in-depth homogeneous specimens with ideally flat surfaces, to multiple scattering corresponding to the Poisson stochastic process, the inelastic scattering being described by the mean free path, etc.; these assumptions enable one to use the Boltzmann-type classical transport equation (see, e.g., Werner, 1996). The simplest solutions then assume that the scattering is restricted to small angles. Program packages utilizing the MC algorithm also rely on the simplifying assumptions mentioned above, except those regarding the homogeneity, semi-infinity, and flatness of the specimen. Otherwise, similar information about the specimen is needed--the differential elastic and inelastic cross-sections or their equivalents, the differential inverse mean free paths. Let us briefly summarize the MC procedure for tracing the scattering of one electron (see, e.g., Ding and Shimizu, 1996). The basic concept is the normalized accumulation function A(x) for some probability distribution function P(x) of a physical phenomenon with one parameter x:
A (x) --
fxx P(x') dx' / l xmaxP(x') dx'. rain '/Xmin
(22)
Obviously A(x) E (0,1) and when uniformly distributed random numbers Tr are taken within this interval and x is calculated from A(x)= R., then after many attempts the assembly of x values obeys P(x). The second basic concept is the rule for deciding which member of a set of n possible phenomena will take place when one must definitely occur. The rule is that
342
MULLEROVA AND FRANK
the ith phenomenon occurs if
n
i
j=l
j=l
s (23)
j=l
j=l
where pj is the probability of the flh alternative. Again, after many attempts the total occurrence of a particular phenomenon corresponds to its probability. Now we can apply Equation (22) to the free path s of the electron provided the scattering probability distribution is that of the Poisson process, i.e., P(S)=(1/)vT)exp(--S/)VT) with 1/)Vr= 1/)Vel+ 1/)~in a s the total inverse mean free path; we simply get s =--)VT lnTr Having determined the free-path section, we use another random number to decide what collision takes place by means of Equation (23) so that Pl = )Vel and P2 = )vin. When simulating the scattering in a compound of m different atoms, the elastic scattering phenomenon can be ascribed to the flh atom according to a j Equation (23) again, now with pj - Cj/)~et, C~ as the atomic fraction. The same procedure can be followed for the inelastic collisions only in alloy-like compounds where the scattering cross-sections can be summed. Otherwise, the compound-specific data for 1/)vin should be acquired. The scattering angle due to an elastic collision is also calculated from Equation (22) with A(x)= 7~, provided P(x) is replaced by dael/dS2; the scattering angle and energy loss for an inelastic event can likewise be found by using d2)~/~1/dr2 d W and dZX/nl/dW, respectively, as the probability P(x). When simulating sophisticated processes such as the formation of an angular resolved energy spectrum of electrons with characteristic energies, in which case only very few of the incident electrons create the relevant signal species, simulation of reversed trajectories can also be used (Gries and Werner, 1990), starting at the detector and finishing at the first inelastic collision. Ding and Shimizu (1996) presented MC modeling of SE generation including cascading processes, which produced energy spectra of SE + BSE emission that fitted the experimental data very well. A detailed study of SE emission from SiO2 by MC simulations was performed by Schreiber and Fitting (2002). These data directly relate to the SEM application. Obviously, both transport function and MC algorithms can be applied on various levels of the physical model, depending of what data for the mean free paths are utilized. For the inelastic scattering, more recent works use the dielectric functions, usually compiled from measured optical data and some dispersion relation, and sometimes a combination of discrete events and continuous slowing down contribution is used or even no discrete events
343
SCANNING LEEM
are considered. For the elastic scattering, all the choices from classical Rutherford cross-sections up to the Mott ones can be found, including the scattering on phonons, as described in previous sections of this chapter. Generally the MC algorithm is capable of working down to very low energies, provided it is completed with adequate scattering data, and only coherent scattering phenomena and effects connected with the energy band structure are excluded. When in the very-low-energy range the scattered electrons are taken as the Bloch electrons within the energy band structure of the target, the electron trajectory, needed for the MC procedure, has to be extracted from E(k), tensor of the reciprocal effective mass ]lm-lll, etc. Then the electron movement in an electric field F is first considered in the reciprocal space as dk/dt=(2ne/h)F, and transition into the real space is made via the real electron velocity (Schreiber and Fitting, 2002)
~(k) - ~ gradkE - 2n 1 + 2~E(k)
k
(24)
with a as the nonparabolicity parameter of the energy band. The MC methods were developed many years ago by Joy (see Joy, 1995) and his programs are widely used. The work of Ding and Shimizu (e.g., Ding and Shimizu, 1996) is important here and simulations carried down to even fractions of eV were made by Fitting and co-workers (e.g., Kuhr and Fitting, 1999; Fitting et al., 2001). The MOCASIM program introduced by Reimer (1996) is also popular. Although the MC approach seems to be much more flexible and universal and enables one to model directly various phenomenological quantities, the necessary number of simulated trajectories grows enormously when any spectrum-like data need to be modeled and the computation time exceeds reasonable limits. Specific solutions to the transport equation are then sought, as, for example, in simulation of the energy spectra of BSE (Reimer et al., 1991).
IV. EMISSION OF ELECTRONS
The previous section provided fundamentals enabling one to comprehend the behavior of the electron emission excited by the impact of primary electrons. We now deal with individual contributions to the total energy spectrum of emitted electrons, shown schematically in Figure 11. This is composed of two main components, SE and BSE emission, which together form the background for electrons with characteristic energies that convey
344
M[ILLEROVA AND FRANK
------
BSE
.
.
.
.
.
Plasrnon |osses ~
AE
l
,
0 I 50 eV m
E SE
l
Ill,
,
l
Ill,
II
l
l [
l
,
l
.
l
Electron energy
,
V
--
:
l
|
l
,l
II
---
-
EmBSE Ep - - - -
FIGURE 11. Typical energy spectrum of electrons emitted under the electron beam impact (for explanation of symbols see text for details).
spectroscopic information. Secondary electron emission and electron backscattering are quite different phenomena, the first of which consists of a stream of particles released from atoms by impact ionization, the most important item within the inelastic scattering, while the latter comprises reflected primary electrons that have undergone some elastic scattering events. Nevertheless, owing to the indistinguishability of electrons, there is no way of separating these groups, except according to some statistical quantities connected with their motion after emission, i.e., with their velocity. Even when considering in simulations that the faster electron leaving the inelastic collision connected with ionization is the scattered particle and the slower is the ionization product, we do not arrive at the correct results because of the existence of processes in which the particles exchange their energies (Fitting et al., 2001). By definition, the separation between SE and BSE emission is situated at the threshold emission energy Et = 50 eV and it is believed that the tails of both distributions, extended beyond Et, compensate each other. This can be the case for high primary energies but, in the low-energy range, the compensation is far from complete, as Fitting et al. (2001) showed by simulating both SE and BSE emissions from Au (see Figure 12). Obviously, below 400 eV the BSE contribution below 50 eV (SBE) strongly exceeds the amount of fast SE above 50 eV (rise), while for Ep > 400 eV the opposite but weaker imbalance exists. This indicates that measurements of both yields, with respect to the 50 eV convention, overestimate 8 below
SCANNING LEEM
345
0.5 0.4 0.,3 0.2 0.1
"1O0
"1000 E [eV]
FIGURE 12. Contribution ~sE of fast SE (E> 50 eV) to the BSE yield ~/, together with contribution 3Be of slow BSE (E < 50 eV) to the SE yield 3, as calculated for Au. (Reprinted with permission from Fitting et al., 2001.)
a certain energy and underestimate it above the same value, while the opposite holds for r/. Nevertheless, any more correct distinction between the two emissions is possible only in simulations but can hardly be made in experiment, so from now on we continue to accept the 50 eV threshold. Naturally, when approaching the very-low-energy range, i.e., somewhere below 100-200 eV, no separation is possible and the total yield cr has to be considered. In this section we will also deal with phenomenological features of emissions such as their yields, energy and angular distributions, information depths, and (for eBSE) the coherence.
A. Electron Backscattering Emission of the backscattered electrons consists of a fraction of the electrons reflected without any significant energy loss, the eBSE emission, while the rest down to 50 eV are electrons with various energy losses. The eBSE peak is a potential source of information about the probability of incoherent elastic scattering, and hence about relations between elastic and inelastic scattering (Gergely, 1986). To acquire this information, it is necessary to measure the eBSE emission yield Tel with respect to the primary current, namely within the maximum possible
346
MULLEROVA AND FRANK
range of emission angles. Measurement on a thin-film-covered substrate under variation of the film thickness is particularly fruitful. The intensity of the eBSE peak generally increases with increasing atomic number and decreasing energy, as does the scattering cross-section Crel. Nevertheless, these monotonic dependences break down below about 1500 eV where the ~ez(E) curves for different Z start to cross each other (Schmid et al., 1983). Owing to multiple scattering inside bulk specimens in SEM, the discrete peaks connected with ionization losses are usually washed out to a smooth distribution curve of BSE modulated with low peaks due to Auger electrons (AE) and to plasmon losses. Only under special circumstances can some very weak ionization loss peaks be observed as, for example, the oxygen ionization peak for a specimen covered with a thin oxide layer; the height of this peak can be up to about 10-3 of the eBSE peak (Gergely et al., 1986). The plasmon peaks can normally be observed in electron spectra taken with an Auger electron microprobe (AEM) and used for analytical purposes as in the transmission mode in EELS. The risk of carbon contamination makes it necessary to examine discrete features in the BSE spectrum solely under UHV conditions. Although the UHV-conditioned modes are not excluded from the scope of this text, we do not consider here instruments equipped with analyzers for signal discrimination according to energy. Hence we will not further discuss the reflection EELS (REELS) method, because within the total detected BSE signal the contribution from discrete peaks is negligible. The overall shape of the BSE spectrum exhibits a very broad maximum at E~s E (see Figure 11). It represents the most probable energy loss of the emitted BSE, and in addition to scattering properties of the specimen, it depends also on the experiment geometry, i.e., on the impact and emission angles. For a tilted specimen and high emission angles (taken from the surface normal), this maximum moves toward Ep (Bauer, 1979) and the same holds for higher atomic numbers (Kulenkampff and Spyra, 1954). Reimer et al. (1991) simulated the energy spectra of the fast electron backscattering into the full half-space for layered structures and demonstrated that the position and height of the spectral maximum sensitively changes with thickness and material of the overlayer relative to substrate. Frank (1992b) presented experimental data for similar layered structures, taken in the low-energy range, together with a model interpreting the position of the BSE spectral maximum in terms of the depth of the film/substrate interface and treating the height of this maximum as proportional to the rate of quasi-elastic backscattering on the interface.
SCANNING LEEM
347
Examination of the BSE spectral maximum also requires using an energy analyzer and hence goes beyond the scope of this review, but the mere existence of this feature is important for SEM because it defines the average energy of the BSE signal species, which is crucial for their detection. Nevertheless, even for homogeneous specimens and normal impact, the mean BSE energy varies within a broad range, and is also affected by the acceptance angle of the detector. Most of the available data are taken with the cylindrical mirror analyzer (CMA) of electron energies, in which the input beam is limited between two cones with a mean emission angle of about 42 ~ In this case one gets E ' ~ s E / E P - 0.83 for A1 and 0.87 for Si but for Cu no maximum develops (Frank, 1992a). Obviously, the energy distribution of BSE should be modeled specifically for a particular detector geometry and the mean energy of BSE can move everywhere above about 0.6Ep. A crucial parameter is the total yield 7/of BSE. With the normal SEM, it is expected that rl will be nearly independent of the energy of the incident electrons and grow monotonically with the mean atomic number of the specimen, giving the broadly used material contrast in the image. Values of r/as well as its energy dependence are available from many sources but we will abandon citing individual experimental studies of the yields because near-complete experimental data from the literature have been collected by Joy (2001) into a database in which data for the low-energy range can also be found. Nevertheless, the scatter in the published data is significant, e.g., for A1 at 1 keV, six values of rl can be found in this database, spanning the interval between 0.134 and 0.2346. It is generally assumed that only the SE yield has to be measured on clean surfaces because of the sensitivity of this parameter toward surface contaminations. Nevertheless, large variations in the measured BSE yields can also be explained only by the surface status. In order to confirm this opinion, a targeted study was made consisting in careful measurement of SE and BSE yields at low energies for 24 conductive elements, both as-inserted into a UHV apparatus and after in situ cleaning by ions. The yields were measured using a device based on a principle published by Reimer and Tollkamp (1980). Here we will quote data from this study (Zadra~il and E1-Gomati, 2002), which have been only partially published hitherto (Zadra~il et al., 1997; Zadra~il and E1-Gomati, 1998a,b). In Figure 13 the data are shown for in situ cleaned specimens throughout the low-energy range down to 250 eV. Obviously, the ~(E) curves for various Z do not tend to one point at the low end of the plot as was shown in some older published results but they do this in the dataset for the as-inserted specimens; in Figure 14 we compare the "clean" and "unclean"
348
MOLLEROV,~ AND FRANK
I . . . . . . . . . .,. . . . . . .
0.5 o.4
.
.
.
,
, I
.
I
0.3 0.2
[
0.1
i
0
1
2
3
4
5
energy [keY] FIGURE 13. The BSE yields measured in UHV under normal incidence of primary electrons onto targets in situ cleaned by an ion beam; values at E - 5 keV correspond to the atomic numbers (top to bottom) 79, 78, 82, 73, 72, 74, 64, 50, 47, 41, 40, 30, 42, 29, 48, 32, 28, 24, 26, 23, 22, 14, 13, and 6 (data provided by Zadra~il and E1-Gomati, 2002). .
.
.
.
0.5
.
.
.
.
.
I
. . . .
'
. . . .
',Pt .......
: .......
'
~
. . . .
'
. . . .
I
. . . .
'
. . . .
I
,
,
,
',
',
',
i ........
Cu :
0.3
. . . .
! ........
i_
_:. . . . . . .
-: . . . .
'
. . . .
1
-Z
Agi 2;==~
i ____J---c-u----~
0.2 . ,
.
.
.
AI
,
,
,
,
,
,
,
,
"I,
,
,
,
,
,
,
,
,
,
,
~
0.1 0 0
1
2
3
4
5
energy [keV] FIGURE 14. Comparison of the BSE yields for normal impact, measured under UHV conditions for as-inserted (. . . . . . ) and in situ cleaned ( - - ) specimens; data provided by Zadra~il and E1-Gomati (2002). d a t a for several elements. It is usual to explain the o b s e r v a t i o n s as a c o n s e q u e n c e o f g r a p h i t i c c o n t a m i n a t i o n a n d oxide layers on as-inserted specimens, w h i c h b e c o m e less t r a n s p a r e n t at low energies a n d increasingly c o n t r i b u t e to the B S E signal. T h e n , b e c a u s e o f the presence o f " s t a n d a r d "
SCANNING LEEM
349
contaminations, very similar data can be obtained for different specimens, at least within their groups of a similar reactivity. Three of these pairs of measurements were studied in detail by simulation of the BSE yields from those specimens, both clean and covered by a contamination layer of a probable composition and thickness (Frank et al., 2000b). It was found that the observed differences in r/due to cleaning can be explained, for example, by the presence of a 3 nm layer of A1203.3H20 on A1 or 7 nm of carbon on Au. The question of the information depth D of BSE emission was also addressed. At a first glance, we can expect a value similar to half the penetration depth, i.e., D ~-Rx/2. Simulation showed that this is approximately so at 1 keV while at 3 keV the information depth is 2 to 4 times smaller than Rx/2 (Frank et al., 2000b) while Joy and Joy (1996) presented this depth as approximately equal to 0.2Rs. These conclusions indicate that, when entering the low-energy range, we have to consider the BSE yield as another surface-sensitive quantity and when interpreting the SEM image we should take into account data corresponding to the vacuum conditions and surface treatment used. In Figure 13 we notice that, just below 5 keV, the r/(E) curves for various Z start to cross each other, which means that the material contrast, i.e., the monotonic r/(Z) dependence at constant E, disappears here and cannot be reliably used for interpretation of micrographs in the low-energy range. This represents an additional threshold separating the low-energy range. In the SLEEM instrument the above-surface electric field has to be kept as homogeneous as possible, which restricts the specimen tilt to within narrow limits. Even so, nonnormal electron impact can occur because of relative enhancement of the radial velocity by deceleration. The BSE yield grows with the specimen tilt 4~ so that, according to MC simulations, for example at 1 keV the ratio r/(80~ ~ reaches 2.9 for A1, 2.3 for Cu, and 1.8 for Au (B6ngeler et al., 1993). The shape of r/(4~) does not noticeably vary with the energy of the electron impact. As regards the angular distribution of BSE, at high energies it is circular in the polar diagram, i.e., r/(| ~(0) cos| At energies as low as 1 keV, the same shape of the distribution was simulated for A1, but for heavier elements (Cu, Ag, Au) the distribution is more 'pointed," i.e., it increases more steeply at small | (B6ngeler et al., 1993). The same change resulted from the MC simulations of Kuhr and Fitting (1999) at 100 eV, though the Au data appeared much nearer to the cosine law than those for Ag. The eBSE distribution was found to be not only strongly pointed toward the axis but also exhibited anisotropy similar to that in Figure 3.
350
MOLLEROVA AND FRANK
B. Crystall&ity Effects In the previous section we discussed the electron backscattering from a specimen behaving like a homogeneous and isotropic continuum. Experimentally, this corresponds to amorphous substances but otherwise averaging has to be made over grains of polycrystals or different orientations of a single crystal. In practice, we usually observe details connected with anisotropy of the scattering properties of crystals. However, electron crystallography is an independent discipline with sophisticated theory and a broad range of experimental data so within this review we can only briefly touch on several key points. For very thin specimens and higher electron energies, the kinematic theory of diffraction can provide useful results, particularly as regards the geometry of the diffraction pattern from which the crystal structure and orientation can be determined; the basic relation is the Bragg equation k-
k o - - g - - g l x *1 § g z x 2* § g 3 x 3*
(25)
in which k0 and k are the wave-vectors of the incident and scattered wave, respectively, and xi* are base vectors of the reciprocal lattice, orthonormal to the base vectors xi of the Bravais lattice of the crystal. This equation represents a condition for constructive interference of waves scattered by individual unit cells in the crystal. In SEM and at low energies, large-angle scattering and multiple scattering phenomena always occur together in the signal generation so that the dynamical diffraction theory is needed. The problem consists in conversion of the incident plane wave into a wave field with the crystal periodicity. This is solved via the Schr6dinger equation with periodic potential and with the solution developed into the Bloch waves. The topic is again discussed in sufficient detail by Reimer (1998) and by authors cited therein. An important step is the development of the crystal potential into a Fourier series with complex coefficients Vu + iVg* where g comprises all points of the reciprocal lattice. The imaginary coefficients Vg* (with the dimension of energy) express the absorption of the electron waves and V0 is the (mean) inner potential inside the crystal. The Bloch waves have the formal appearance
~rj -- Z aj(g)exp[Zrti(kj + g)r]
(26)
g
where aj{g) have the periodicity of the crystal potential. The index j should run over all points of the reciprocal lattice but in practice it is sufficient to
S C A N N I N G LEEM
351
consider only n beams for which the lattice points are near enough to the Ewald sphere. The incident wave then splits into n 2 partial waves forming n Bloch waves. On substituting Equation (26) into the Schr6dinger equation, we get +
2m
Z Vhaj(g- h) - 0
(27)
he0 where K = h-l[2m(E + V0)]1/2 is the length of the incident wave-vector inside the crystal. Solution of Equation (27) gives n values of kj. and n 2 values of the amplitudes aj(g) for the incident wave K and, naturally, at least two beams should be considered of which that of g - 0 is the primary beam. It is quite obvious that the intensity of such a scattered wave is anisotropically distributed, which projects itself into anisotropy of the emitted signals so that their cosine or similar monotonic distributions become modulated. The directions ke of enhanced intensity can be estimated by the Bragg equation, now in the form of k e = K+g. Observable consequences of these phenomena include dependence of ~ on the crystallinic orientation (i.e., on the specimen tilt or on orientation of a crystal grain) and also some structure modulating the r/(| distribution. Variations in r/due to the orientation can be a source of grain contrast at polycrystals. In the two-beam approximation and assuming that the Bloch waves do not interfere, we get (according to Reimer, 1998) for variation in the backscattering coefficient
A_____9_~ = r/
~ co + ~/~g 2rtD 1 + 092- ~ / a
(28)
where ~g is the absorption length, ~g-hv/2Vg, and co=S~g is a dimensionless factor in which s = Isl characterizes deviation from the exact Bragg position (distance of the reciprocal lattice point from the Ewald sphere) and ~g = hv/2 Vg is the extinction length. Further, D is the (already introduced) information depth of the backscattered signal, D = ~I/NaB, with aB as the cross-section for scattering through angles greater than 90 ~ Because at least down to hundreds of eV D decreases with decreasing energy faster than ~g, we find that, among other effects, the grain contrast increases at low energies. Modulation of r/(| includes all the electron diffraction phenomena that have proved to be sources of extremely interesting image signals in LEEM. In the low-energy range, the Bragg angles 08 = arcsin O~/2dh~l)(with dhkt as the interplanar distance in the real crystal) are still less than 90 ~ and no
352
MOLLEROVA AND FRANK
regular diffraction pattern is formed by backscattered waves. But an important phenomenon is the formation of EBSP (electron backscattering patterns) whereby diffused BSE upon their return toward surface diffract on sets of atomic planes and form Kikuchi bands and lines, which are in fact intersections of so-called Kossel cones with the observation plane. The Kossel cones comprise all the vector directions fulfilling the Bragg equation so that one cone contains k0 and the other k, both having g as the cone axis. In EBSP these features can be visible when the backscattered electron suffers only single elastic scattering before emission. Thus, a good contrast of EBSP can be achieved solely at high tilt angles around 70 ~ and also at higher electron energies. Nevertheless, some modulation of r/(| should be present even in the low-energy range but to the authors' knowledge, no successful observation has been made yet. At energies of the order of hundreds of eV, the Bragg angles start to exceed 90 ~ and true diffraction patterns can be formed. At the same time, the penetration depth shrinks so that electrons interact with a nearly twodimensional lattice and the Bragg equation has to be fulfilled only for vector components parallel to the surface. In other words, the reciprocal lattice, normally three-dimensional with lattice points of a size inversely proportional to dimensions of the real crystal, is now filled with "rods" perpendicular to the surface. In fact the real situation is usually between the two marginal cases, so that the "rods" are modulated in "thickness" and the third-dimension condition still has to be considered. Formation of a LEED pattern with sharp diffraction spots requires the use of a beam aperture below 1 mrad as in transmission microscopy. As will be shown below, in SEM the optimum beam aperture, tuned to ultimate resolution, can approach the 1 mrad level but after deceleration to very-low-energy, the aperture grows to tens of mrad. Consequently, the diffraction spots extend to discs, as in CBED conditions in STEM. It is a matter of debate whether these mutually overlap, which would further enhance the signal. A position-sensitive multichannel detector situated above the specimen (or in a side position when a through-the-lens detection system, to which the signal electrons are deflected, is employed) enables one to observe the local deviations from fulfillment of the diffraction condition. Even a single-channel integral detector will show as brighter those areas where, at the energy used, the Ewald sphere just crosses some reciprocal lattice point. However, owing to dynamical effects, additional maxima of the signal can appear. This imaging mode will be illustrated in Section VIII. Irrespective of the beam aperture, effects connected with channeling of the Bloch functions, like formation of Kikuchi lines, take place and are visible in the phenomena outlined above, because their geometry is connected with the crystal structure and not with the beam shape.
353
SCANNING LEEM
C. Coherence within the Primary Beam Spot A crucial condition for constructive interference of waves scattered from individual atoms is coherence within the primary spot. This should be assessed in connection with the energy and angular spreads of the beam that determine whether all contributions from the illuminated spot are amplitude summed. As discussed by Buseck et al. (1988) for STEM, no amplitude addition between neighboring pixels can appear. The coherence conditions for a single static spot were discussed by Frank et al. (1999). The energy spread in the primary beam is mainly given by the type of the electron gun and varies between 0.2 eV for a field-emission cathode at room temperature up to about 2 to 3 eV for thermoemission from tungsten, provided we neglect any additional spreads generated by e-e interactions in crossovers. According to Born and Wolf (1975), the coherence condition for the path difference As, i.e., for the size Dc of the coherently illuminated area, is
Dc - I A s ] << (7,~.,2
~,~
2.45 ~
[nm; eV].
(29)
/__k/5
The initial source size, also connected with the emission type used, gives the maximum diameter of the coherently illuminated diaphragm. If we tolerate a decrease to 88% in the complex degree of coherence from the center to the edge of the illuminated area, then a quasimonochromatic uniform source of angular radius y - p/x (see Figure 15) illuminates "nearly coherently" a circle of a diameter 2r=0.16()~)/?, (Born and Wolf, 1975). Hence a further coherence condition is ,o _<
0.08(i.) ly o
~
0.98
[nm; eV]
(30)
-- lyo~
In diffraction experiments the so-called "transfer width" (see Woodruff and Delchar, 1986) plays a similar role to that of the beam coherence area. In order to understand this concept, we have to recall that the reciprocal lattice points have a "size," which is inversely proportional to the crystal dimensions. Hence the diffracted beams have a finite angular size corresponding to the dimensions of the area from which the amplitude addition takes place. If any imperfections in the primary beam exist, such as energy and angular spread, that cause a change in the wave-vector Akll, then they also correspond to some distance on a surface, just as we get the surface periodicity length from the Bragg condition, dhk-- 1/Akll. These lengths are analogously defined as w = 1/AkiN, and determine maximum distances over
354
MOLLEROVA AND FRANK
!2p
x
. . . . .
r . . . . . . .
,,-
_
! 9r
FIGURE 15. Definition of quantities used in the assessment of the primary beam coherence.
which variations in the surface periodicity can be detected. In other words, Akll represents now a dispersion caused by a finite aperture and energy spread of the illuminating beam. Thus, the area of addition of amplitudes is limited by "angular" and "energy" transfer widths Wo and wE so that
Dc
< wo
-
~. 0.61 2oe cos0 >- ot
Into; eV]
(31)
and 2E
D c < wE -- dhk ~ . AE
(32)
Later we will see that in a normal SLEEM configuration all these conditions for sufficient coherence within the primary spot can be satisfied. The diffraction spots can overlap in the radial direction when their angular size, A0 ~ )~/dhk COS0, is larger than 2or. This can easily happen and then further intensity increase is achieved. D. S e c o n d a r y E l e c t r o n E m i s s i o n
Secondary electrons are released from the target atoms by impact ionization, which forms a substantial contribution to quantities characterizing
SCANNING LEEM
355
the inelastic scattering. According to conclusions drawn from results of momentum-resolved coincidence spectroscopy, the main source of SE is decay of the valence band excitations caused by large momentum transfer spatially localized scattering events (Drucker et al., 1993). Further intensive SE generators include decay of volume and surface plasmons; the yield from the electron-electron collisions is substantially weaker. Upon release from an atom, the internal secondary electron possesses kinetic energy (taken with respect to the bottom of the conduction band) of the order of 101 eV. For example, Schreiber and Fitting (2002) studied in detail the SE emission from SiO2 and found the mean initial kinetic energy to be 13 eV. Owing to further impact ionization and cascading processes, the energy of the SE dropped below 10 eV within 10 fs. Then, scattering on phonons dominated and after 200 fs the electrons were more or less thermalized so that their energy approached 3~:T/2, i.e., approx. 40 meV at room temperature. Finally, electron-hole recombination took place and within 1000 fs the released electrons were almost all recombined or trapped. Emission of a SE has, therefore, to take place within a very short time after its generation. Data important for understanding the SE signal in SEM were reviewed by many authors, e.g., Bruining (1954), Kollath (1956), Dekker (1958), Hachenberg and Brauer (1959) and Seiler (1983). The measured SE yields are contained in the database of Joy (2001) and we will quote also the data from the study targeted at the determination of the influence of the surface cleanliness (Zadra~il and E1-Gomati, 2002). The SE yield 3 is relatively low at the energies normally used in the SEM; we can verify in the database of Joy (2001) that at 20 keV, 3 < r/for all except the lightest elements, for which both yields are roughly equal. But at low energies, 6 is significantly larger than r/--this relation creates another crucial distinction of the low-energy range. Similarly, the information depth of BSE is normally much larger than that of SE but this relation also reverses. According to the simulations of Kuhr and Fitting (1998), the relation between maxima of the depth distributions for SE and BSE from Ag is mutually opposite for electron energies 3000 eV and 100 eV. The maximum SE yield 3m, achieved at a certain energy of the incident electrons Em (located between 100 and 900 eV), remains within 0.5 to 1.7 (Seiler, 1983) or 0.6 to 2.1 (Zadra~il and E1-Gomati, 2002) for metals. For insulators, owing to the extended escape depth of SE, the yield can reach values even higher than 10 (Seiler, 1983; Joy, 2001), for alkali halides in particular. In Figure 16 a set of data similar to that in Figure 13 is given; these are now values of 6 for the same selection of 24 conductive elements.
356
Mf]LLEROV~t AND FRANK
2.0
5 1.5 1.0 0.5
0
,
,
,
,
,
,
,
,
4
5
2
1
3 energy [keY]
FIGURE 16. The SE yields measured in UHV with normal incidence of primary electrons onto targets in situ cleaned by an ion beam; values at E = 1 keV correspond to the atomic numbers (top to bottom) 64, 13, 40, 78, 79, 72, 47, 30, 82, 50, 14, 29, 24, 48, 74, 73, 28, 32, 42, 26, 22, 41, 23, and 6 (data provided by Zadra~il and E1-Gomati, 2002).
i i ii[i ii i ii i ii
2.0
5 1.5 1.0 0.5
i
0
,
, ~
,
,
,
,
,
,
,
,
,
,
4
5
1
{
2
3 energy [keV]
......
=
FIGURE 17. Comparison of the SE yields for normal impact, measured under UHV conditions for as-inserted (. . . . . . ) and in situ cleaned ( - - ) specimens; dashed curves correspond to (top to bottom) Ag, A1, Pt, Cu, and C at 1 keV (data provided by Zadra~il and E1-Gomati, 2002).
SCANNING LEEM
357
Further, in Figure 17 the same pairs of measurements are given as in Figure 14, i.e., for the specimen as-inserted into UHV and after being ion-beam cleaned. Here we notice a pronounced similarity between the as-inserted curves, which obviously corresponds to similarly contaminated surfaces although the specimens were thoroughly precleaned and measured under clean conditions. A semiempirical theory of SE emission, summarized by Seiler (1983), gives a universal (i.e., specimen-independent) curve
3m-- "
~
1--exp
--2.3 Emm
"
(33)
It is also stated that for metals, 8m/E m is constant (due to the proportionality of both quantities to j4/5) and approximately equal to 2 x 10-3 eV -1 (Ono and Kanaya, 1979). Nevertheless, data tabulated by Seiler (1983) do not indicate constancy of 3m/Em and when extracting this ratio from Figure 13, we find that its average value is around 0.002 eV -1 but the values are scattered between 0.0012 and 0.0053 eV -1. All sources of data confirm that in their Z dependences both ~m and Em exhibit a modulation corresponding to the periodic system of elements. This modulation is apparent even when drawing a 6(Z) curve for an arbitrary energy value (Zadra~il and E1-Gomati, 1998b). At incident electron energies sufficiently higher than Em, the SE yield decreases as E -~ (Drescher et al., 1970), which is the energy dependence of the Bethe stopping power. Near and below the yield maximum, no universal relation exists except Equation (33). The energy distribution of emitted SE has a strong maximum at energy E~E (see Figure 11), which is smaller for insulators than for metals, for which it moves between 1 and 5 eV, while the width of this distribution, measured at half maximum, ranges from 3 to 15 eV (Schfifer and H61zl, 1972). Ding and Shimizu (1996) verified that the energy distribution does not depend strongly on the emission angle. The dependence of the position and width of the distribution peak on the material and its surface status were studied by Dietrich and Seiler (1960) and Joy (1987), and others. Fitting et al. (2001) found, again for SiO2, that the value of E~'E decreases with increasing escape depth of SE. Chung and Everhart (1974) presented a simple theory leading to a relation for ~(EsE) for metals. They supposed the surface potential barrier fully transparent for EsE> 0 (with EsE measured from the vacuum level) and nonpenetrable otherwise, and the SE generation to be isotropic and depth independent. The resulting
358
MfJLLEROVA AND FRANK
expression was
dNsE dEsE
~ = K - -
1 ESE E (EsE + q~W)4
(34)
(where 4~w is the work function and K is a material constant), giving E'~E -- 4)w/3. For our next considerations, we need some "mean" energy of SE; from Equation (34) the mean value of ESE is 2 4~w. However, the mean
value overestimates the contribution of fast SE so that it is more reasonable to take the median, which is equal to 4~w here. Thus, for detection considerations, we can use 3 to 5 eV as the typical energy of SE. A more exact theory would require incorporation of processes of SE generation, diffusion inside the target, and penetration through the surface barrier. Reimer (1998) reviewed calculations made for aluminum (see, e.g., Bindi et al., 1980) and hinted at anisotropy of the internal SE release, which is afterwards quickly randomized, owing to the short mean free path, to the cosine distribution. In practice, the distribution 8(| cos | is observed generally at all instances (see, e.g., Kanaya and Kawakatsu, 1972). Nevertheless, with single crystals some structure again appears on the angular distribution, caused by channeling of the Bloch functions as we mentioned for the BSE emission (see, e.g., Burns, 1960). The smooth energy distribution described by Equation (34) can exhibit some additional structure at energies equal to energies of plasmons. Everhart et al. (1976) observed this structure with aluminum and for an atomically clean surface they found that the energy distribution was broadened and contained some features at energies corresponding to surface and volume plasmons. Nevertheless, after very slight oxidation the structure not only disappeared but also the main peak became much narrower. This indicates that the SE generation via decay of plasmons is sensitive to the surface status and is much weaker at "real" surfaces. At high energies the dependence of 8 on the specimen tilt angle 4~ is very important, causing the most pronounced contribution to the image signal, owing to which the SEM image acquires its three-dimensional appearance. The proportionality can be written as 8(4~)oc secn 4~ with n decreasing from about 1.3 to 0.8 throughout the Z scale (Seiler, 1983). An extreme demonstration of this dependence is so-called edge effect, i.e., a strong overbrightening of side walls of surface steps that dominates micrographs at conventional energies. The phenomenon is simply caused by the SE escape depth being shallower than the penetration depth of primaries, owing to which any inclined facet represents an additional emitting surface. Thus, the edge effect should disappear at low energies (see Figure 18) near to Em for the maximum SE yield where all generated SE are emitted; this was
SCANNING L E E M
o 0 . 5 keV
C) ,._.,.
9 0.5 keY
AI
9 1 keY 9 2 keY 9 5 keY
I3
0J
0
'J
LI'iIIj
20
Au
9 1 keY 9 2 keY 9 5 keY
13oo
9 10 keY
1 .t.,,_.=.=i--.=~
359
9 1 0 keY
.-e~'2
-
J
40
J
tilt angle (I) [deg]
J--
60
j
'
80
0
0
'
J
20
'
4
b
'
60
tilt angle (I) [deg]
FIGURE 18. Experimental data for tilt-angle dependence of the SE yield. (Reprinted with permission from B6ngeler et al., 1993.)
quantitatively verified by Pejchl et al. (1993). Consequently, the SE contrast at low energies is restricted to the "shadowing" connected with the usual side position of the detector and the image becomes more "flat" (see Joy and Joy, 1996). When exciting SE from a single crystal, the monotonic 3(4~) dependence again acquires a structure. This is normally comparable with that of the BSE yield, A~/r/ (see comparison made for Si(111) by Seller and Kuhnle, 1970) but toward low energies A3/3 does not grow so distinctly as A~/~ does. Hence any grain contrast in SEM micrographs at low energies are more probably caused by the BSE emission anisotropy. Further studies regarding the angular distribution of 3 include those of Salehi and Flinn (1981) and Libinson (1999). An important collection of experimental results concerning the SE emission anisotropy has been acquired by using UHV SEM instruments equipped with detectors featuring an enhanced angular sensitivity, usually achieved by suppression of SE emitted off the direction toward the detector. Then, Homma et al. (1993) observed alternating 2 x 1 and 1 x 2 domains in subsequent atomic layers on Si (100) as well as reconstructed 7 x 7 domains coexisting with nonreconstructed remains of 1 x 1 phase on Si (111). Domains were visible even at an electron energy of 25 keV but enhanced contrast was demonstrated at 2 keV. Similar instrumentation was used to visualize surface atomic steps, e.g., those on Si (111) (Ishikawa et al., 1985) or on an oxidized Cu surface (Bleloch et al., 1989). Obviously, with careful in situ treatment of the specimen surface, even in the "incoherent" SE imaging many phenomena can be observed which would intuitively be
360
MULLEROV!i. AND FRANK
expected to be perceptible solely by diffraction contrasts in the LEEM method. An important characteristic is the mean escape depth )~esc of SE, which governs the information depth of the SE image. The probability of escape Pesc is generally considered to be exponentially dependent on the depth, i.e., Pesc~ exp (--Z/~,esc). Values of ~esc range between 0.5 and 1.5 nm for metals and between 10 and 20 nm for insulators while the maximum escape depth is T TM 5Le~ (Seiler, 1967). The larger values of Le~c for insulators are in accordance with the enhanced SE yield from them. Fitting et al. (2001) found for SiO2 that ~esc decreases with increasing SE energy--for EsE < 3 eV it amounted to about 10 nm while for Ese > 20 eV it dropped below 1 nm. If the escape depth is brought into relation to the electron range R, we get the maximum SE yield at R-2.3Xesc (Seiler, 1983). At higher energies the SE generation extends to depths from which no escape is possible while at lower energies the generation rate (the integral of the stopping power along trajectory of the incident electron) diminishes. The shallow escape depth, together with sensitivity toward ionization energies of least bound electrons, makes the SE emission very sensitive to the surface status, its cleanliness and contamination, and also to the radiation damage. At conventional SEM energies, the secondary electron signal is composed of so-called SE1 and SE2 contributions, the first being excited directly by PE while the latter are due to BSE returning toward the surface. While SE1 escape from an area the diameter of which is approximately (d2 + ~e2sc)1/2 with de as the primary spot size (see, e.g., Everhart and Chung, 1972), the SE2 signal emission spot is broadened by lateral diffusion of BSE so that the specimen response function consists of two bell-shaped features of different width. We will discuss this later in connection with the image resolution but now let us mention that the total SE yield is usually written as
(~ - - ~ P E + ~ B S E - -
~0[secq~ -+- fl(q~)~]
(35)
where 30 is the SE1 emission at normal impact of PE and fl(~b) denotes the ratio of the SE yields between PE and BSE. The ~b dependence of I3 is decreasing (Seiler, 1983) and /3> 1 because BSE have lower energies than PE and also their trajectories are generally more inclined with respect to the surface normal. Above about 10 keV, we get fl~-2.5 with only weak material and energy dependences. For low energies, when the electron range approaches the escape depth of SE, this approach, as well as any distinction between SE1 and SE2, becomes questionable. Nevertheless, at least at the beginning of the low-energy range, i.e., down to, say, 2 to
SCANNING LEEM
361
3 keV, Equation (35) can be considered, probably with an increasing value of/~. The role of BSE in the SE emission has been studied by numerous authors (e.g., Kanter, 1961; Kanaya and Kawakatsu, 1972; Joy, 1984; Hasselbach and Krauss, 1988; B6ngeler et al., 1993). For us the distinction between SE1 and SE2 is of minor importance because in SLEEM the standard detectors acquire the total emission cr = • + r/. Nevertheless, we should be aware that, even at low energies, the SE yield from surface films depends on the underlying substrate and when the two materials have very different Z, the change in 3 with the film thickness is very strong so that in fact the SE2 contribution prevails over that of SE1, see, e.g., measurements of Thomas and Pattinson (1970). As regards the noise in SE emission, it is usually considered to follow the Poisson distribution. This was proved for energies below 250 eV (Seiler, 1983) but at higher energies some excess noise content is found (see Reimer, 1971) because of the SE2 contribution. This question does not seem to have been fully answered. Finally let us mention that SE emitted from ferromagnetics are spin polarized (Kirschner, 1984). The degree of polarization is nonnegligible even for very low-energy electrons and further increases with E, with the highest polarization found for the slowest SE. The effect is explained by the different reflectivity of electrons with different spin orientations. This phenomenon would enable one to observe the domain contrast if a detector of polarized electrons was available.
V. FORMATION OF THE PRIMARY BEAM
We have already touched on the important circumstance that in SEM the specimen represents a part of the imaging system. The information collected, coming from the entire interaction volume of the primary beam, is ascribed to a single point labeled by pixel coordinates so that the response function of the specimen, i.e., distribution of the signal excited by a monochromatic infinitely narrow incident pencil, has to be taken into account when assessing the resolution. However, incorporation of the specimen properties prevents us from drawing general conclusions about the instrument quality so that it is usual to evaluate an "intermediate" quantity, namely, the current distribution in the primary beam spot entering the specimen. We will do the same and afterwards we extend the discussion toward the concept of the "real" resolution on a particular specimen.
362
MULLEROVA AND FRANK
A. The Spot Size
Within the scope of this text, we cannot go into details of the electron optical theory of the SEM column, of the lens aberrations and their combinations, and related problems. Let us only mention that correct results, particularly for coherent or nearly coherent illumination by various types of field-emission guns, can be obtained only by wave-optical theory of the electron probe formation, which regards lenses as diaphragms filled by a phase shifting medium that deforms and trims the wavefronts. However, our aim is to explain, using relations as simple as possible, the specifics of the low-energy spot formation and hence we will utilize the simplest approximate figures obtained from geometric optical theory. For more details we can refer to Reimer (1998) and particularly to an exact analysis of the topic made by Hawkes and Kasper (1996b). We will simply consider the primary spot as a convolution of the current distribution within the demagnified image of the gun crossover with discs of confusion of the basic aberrations. Assuming the astigmatism and defocusing aberrations fully corrected, we take into account contributions to the spot size expressed in the form of discs of confusion the sizes of which are
dG --
41) 1/2Of-1 ,
~
ds - KsCsot 3,
AE dc - K c C c --if- or,
do - KD~.Ot-1
(36) where dc is the demagnified crossover, ds, dc, and do are the discs of spherical, chromatic, and diffraction aberration, respectively, I is the beam current, /3 is the gun brightness, ot is the specimen-side angular aperture of the primary beam, Cs and Cc are the coefficients of spherical and chromatic aberration, respectively, and Ks, Kc, and KD are numerical factors dependent on the model of the spot formation. Here the leastconfusion planes are assumed for spherical and chromatic aberrations and the final aperture-limiting diaphragm is considered uniformly illuminated. When using the full beam diameters in the least-confusion planes of spherical and chromatic aberrations and FWHM of the Airy disc for the diffraction aberration, we get the numerical factors as Ks = 0.5, K c = 1, and KD=0.6. The next step is to select a summation rule for combining the contributions from Equation (36) into the overall spotsize de. It is traditional to consider the ray radii in the individual discs as mutually independent random variables with normal distributions. Then the
SCANNING
LEEM
363
summation rule is given by a convolution of Gaussian functions the result of which is also Gaussian and
4=4+4+4+d
.
(37)
In fact, the individual contributions are neither independent nor normally distributed so that Equation (37) provides only a rough estimate of dp. A more realistic but still reasonably simple relation is obtained by defining the disc sizes as the diameter encircling some current fraction. Using this approach, Barth and Kruit (1996) derived the summation rule (for 50% of encircled signal) 1.3/4 . --1 3 2/1.3
+d 2
(38)
and determined modified values of the numeric factors, namely Ks-O.18, Kc-- 0.34, and KD -- 0.54. Other summation rules exist that provide more exact but at the same time more complicated relations for the spotsize (see, e.g., Kolafik and Lenc, 1997) but we shall use the summation rules in Equations (37) and (38) and compare their results. First of all let us make the following simple observation: when the electron energy E decreases, the wavelength increases as )~o(E -1/2. This causes the Airy disc to extend and in order to suppress the impact on resolution, we have to adjust the beam aperture to the same slope ot c~ E -1/2. But then the spherical and chromatic aberration discs grow as dsoc E -3/2 and also dc oc E -3/2. The same energy dependence would in turn apply to the total spotsize dp, fully preventing any use of very low energies. To compensate this, an objective lens would be needed with aberration coefficients, Cs and Cc, proportional to E 3/2. However, the normal magnetic lenses have energy-independent aberration coefficients. It is true that, for example, for weak lenses Cs is proportional to f3 (Glaser, 1952), i.e., in fact to E 3, but after changing the beam energy we have to refocus to the same specimen plane and hence to get the same f and also the same Cs. Consequently, the spotsize enlarges at low energies. The optimum angular aperture Otoptfor achieving the ultimate resolution d~' is simply calculated from the relation adp/aot-O. In Figure 19 we have the function Otopt(E) plotted from the beam energy 15 keV downwards for both above-given summation rules and for two model SEM instruments of a different quality. These are defined in order to span the current instrumentation scope; the first, "TEG SEM," represents old instruments probably not marketable any more but still serving in plenty of laboratories
364
MI]LLEROVA AND FRANK 9
9
9
|
.
.
.
.
.
.
i
,
9
9
,
9
!
,
101 FEG
-o
'
..-H''"
:
s ; ' "
t,-
E
,.__,
m ,--1 0 0 1E (D Q.
10 -1 10 -3
I
10 -2
i
i
10 -1
9
10 0
.
9 i
101
energy [keV] FIGURE 19. The optimum angular aperture, Olopt,for the smallest spotsize, plotted versus electron energy. TEG SEM and FEG SEM denote the two sets of SEM parameters given in the text, the dashed line corresponds to the summation rule (37), and the full line to the rule (38).
while the other, " F E G SEM," is for high-quality modern devices. The parameters were chosen as /3-105 A cm -2 sr -1, I - 5 pA, A E - - 2 eV, C s - 50 mm, C c - - 2 0 mm for TEG SEM, a n d / 3 - 109 A cm -2 sr -1, I = 100 pA, A E = 0 . 2 eV, Cs= 1.9 mm, C c = - 2 . 5 mm for F E G SEM. Naturally, there might be queries about individual parameters but as we will see, the basic trends that we are now seeking for are independent of these details. One general trend is obvious already from Figure 19: along the low-energy range, all curves progressively acquire the same slope Otopt(xE 1/4. T h i s behavior can be easily obtained from Equation (37) when we retain in it only members growing at low energies, i.e., dc and dD. When substituting ot c~ E 1/4 into all terms listed in Equation (36), we get the proportionalities dG (X E -1/4,
ds (x E 3/4,
dc (x E -3/4,
dD (x E -3/4
(39)
so that the influence of dc and dD dominates and hence the same slope can be expected for de. In Figure 20 is shown the dp (E) plot for ot = Otopt,which confirms the said behavior, again independently of the summation rule and instrument parameters. The foregoing very simple considerations have yielded the general relation for SEM, namely the proportionality of the spotsize to E -3/4. This says that when we want to turn from the conventional energy like 15 keV to units of eV, the resolution in nanometers deteriorates to the same number
S C A N N I N G LEEM
365
104 103 rE ~
N
10 2
O ~
10
100 ,
10-3
,
,
|
10-2
,
,
,
|
,
,
,
I
1'0-1 100 energy [keY]
,
,
,
,
1;01
FIGURE 20. The ultimate spotsize, d~', for the optimum angular aperture Otopt, calculated for two sets of SEM parameters denoted by TEG SEM and F E G SEM (see text) from the summation rules (37) ( . . . . . . ) and (38) ( - - ) .
in micrometers, i.e., below the level of a standard optical microscope. The proportionality to E -3/4 s e e m s to be broken by parameters of some recent microscopes that guarantee the spotsize at 1 keV only about three times larger than that at 15 keV but the improvement is achieved at the cost of shortened working distance, reduced current, and other restrictions (see, e.g., Nagatani et al., 1987). In general, a conventional SEM without aberration correctors can work at acceptable quality of micrographs down to 1 keV. Because the E -3/4 slope does not depend on the instrument class, we will not discuss in detail the methods of optimizing the objective lenses and detection systems toward improved resolution at low energies. These mostly rely on placing the specimen very close to or even inside the magnetic field, which in turn brings some limitations on other parameters of the microscope operation. Among possible configurations, the so-called single-polepiece lens (Mulvey, 1984), with the second polepiece shifted far from the optic axis and the primary spot, attracts the most attention. Various configurations based on the single-polepiece principle were studied by Pawley (1984), Bode and Reimer (1985), Shao (1989), Mtillerovfi et al. (1989) and Ximen et al. (1993), and others. Some setups achieved very low aberration coefficients like the Cs=O.15 mm and C c = 0 . 5 5 mm of Tsai and Crewe (1998).
366
MOLLEROVA AND FRANK
B. Incorporation of the Retarding Field A qualitative step forward as regards possibilities of the SEM operation throughout the full energy scale was achieved by introducing nonconstant beam energy along the column. The idea is to form and transport the beam at high energy and only close to the specimen to retard it to a final low energy. The underlying principle consisted in one property of the immersion electrostatic lenses, namely that the magnitude of their aberrations corresponds to the higher of the electron energies on either side of the lens. So an immersion lens, i.e., an electrostatic lens with different potential on the marginal electrodes, can be inserted into the end part of the column with the negatively biased electrode toward the specimen. Fundamentals about configurations utilizing this principle were studied in detail by Frank and Mfillerovfi (1999). For estimation of aberrations of the immersion lens we use the approximate equation (Lenc, 1995)
1fzil[(I)~z)]1/21(I)~Z o0]
Cs ~ Cc ~-~
)
~
dz
(40)
where interval (z0, zl) spans the transition region of ~(z) between ~0 and ~1. If we consider the electrostatic field strength abruptly changing in the planes of flat electrodes held on ~0 and ~l, we get
Cs ~ Cc ~
g + ( ~ / _ ~ + 1) 2
1-
(41)
(see also Lencovfi, 1997) with w and 1 being the distances between the specimen and the first electrode and between electrodes, respectively, and k the ratio of electron energies on either side of the lens, i.e., k = Ee/E (Ep is the beam energy in the SEM column and E = Ee + e Ub, with Ub being the retarding potential, is now the lowered energy of impact on the specimen). In Figure 21 we see that the approximation (41) differs appreciably from results obtained when substituting real potential distributions into Equation (40) but on its basis we still can make at least one simple consideration. At very low energies, i.e., for high values of k, both Cs and Cc approach w/2. So they are still independent of energy but can be quite small. However, for w small enough both coefficients are approximately proportional to Ilk = (l/Ee)E and hence diminish with decreasing energy, as we required in the previous section. Of course, the aberrations according to Equation (41) combine with aberrations of the magnetic objective lens but
SCANNING LEEM 10 0
.....
---
......
---
.....
367
; - - - - - -:- - - - - - - - -ii
Cs/I
~.r""
Cc/I
f
C Jl
,
,
1 0 -1
10 -2 |
i
,
0.3
|
,
0.6
,
,
0.9
i
1.2
working distance, w/I
FIGURE 21. The aberration coefficients, Cs and Cc, of the immersion electrostatic lens plotted versus the working distance w with both axes scaled by the length of the retarding field I. (a) Approximate Equation (41) for abrupt field transitions; (b) and (c) calculation from Equation (40) for real potential distributions with the first electrode (nearest to the specimen) of a thickness t--0.1 l (b) and t =0.2 l (c). those are in the summation rule weighed by k -3/2 o(E 3/2 (Lencovfi, 1997), which is exactly the energy dependence that fully suppresses the resolution worsening at low energies. Obviously, the immersion objective lens eliminates deterioration of the objective lens parameters for slow electrons and introduces its own but weaker tendency to a larger spotsize. Figure 22 shows the most popular design of a compound lens consisting of the magnetic focusing lens and electrostatic retarding lens (Frosien et al., 1989), which is, together with the above-lens detector, also called M E D O L (magnetic-electrostatic detector objective lens). Authors report improvement in the aberration coefficients from C s = 59 mm and C c = 15 mm to C s = 3.7 mm and C c = 1.8 mm at the immersion ratio k - 1 7 so that a resolution of 5 nm at 500 eV was achieved (Martin et al., 1994). This design was also used in the first and still the only commercial SEM with the retarding field element and subsequently its parameters have been further upgraded. With a similar configuration, Knell and Plies (1998) obtained 3 nm at 1 keV and 9 nm at 200 eV. The MEDOL-type lens was preceded by a purely electrostatic (three-electrode) lens by Zach and Rose (1988), called E D O L (electrostatic detector objective lens, see Figure 34); further data were then published by Zach (1989) and Zach and Haider (1992). For a beam energy of 8 keV inside the column, they applied the electrode potentials-7.5, + 7, and 0 keV (when proceeding from the specimen) and
368
MULLEROV]i AND FRANK
i~ ~ ;~.....
specimen
FIGURE22. Combinedmagnetic-electrostatic (compound) objective lens. (Reprinted with permission from Frosien et al., 1989.) hence reached a landing energy of 500 eV for which a resolution of 7 nm was reported. Other configurations on a similar principle include the use of a so-called "booster," i.e., a tube around the optic axis between the anode plane and the lower polepiece of the objective lens, insulated and held at a high positive potential (Beck et al., 1995) so that its lower end fully corresponds to the arrangement in Figure 22. Preikszas and Rose (1995) explored the possibilities of optimizing compound lenses and took into account maximum feasible magnetic and electric fields (they considered as limiting values 5 k V m m -1 and 1 T), tolerable fields at the specimen surface, bore diameters in electrodes and polepieces, maximum immersion ratio, and energy spread in the beam. Also Khursheed (2002) examined the aberrations of a set of the compound lens configurations. Let us only briefly mention that, adjacent to the SEM instrumentation area, is the family of IC testers, i.e., specialized scanning devices for inspection of semiconductor structures and measurement of critical dimensions on them (see, e.g., Ezumi et al., 1996). Their recent versions nearly exclusively work in the low-energy range around 1 keV, employ
SCANNING LEEM
369
various combinations of the compound lenses with energy filters (e.g., Frosien and Plies, 1987) and detectors, and achieve resolution comparable with those mentioned above. Practice has confirmed the advantages of using the retarding field principle, i.e., immersion or compound lenses, for SEM in the low-energy range. In recent commercial instruments acceptable imaging parameters have been achieved down to about 200 eV and the limit for reported laboratory configurations and IC testers is similar. A separate class is formed by the first operated versions of aberration correctors. These are capable of achieving the resolution quoted above even in a device with the beam energy constant within the column. Possible corrector configurations were reviewed by Rose (1987), Rose and Preikszas (1992), Hawkes and Kasper (1996a) and Hawkes (1997). The aberration correctors are, nevertheless, mostly applied to STEM, TEM, and LEEM instruments where the specimen influence on the real image resolution is either nearly negligible or does not apply so that any spotsize correction is more efficiently projected into the final result. Only a few applications in SEM have been reported yet; these were briefly reviewed by Frank (2002). C. The Cathode Lens In the previous section we noticed that for a very short working distance w of the retarding immersion lens, the aberration coefficients diminish with decreasing electron energy. A promising alternative is thus to choose w = 0, i.e., to apply the retarding potential directly between the specimen and some anode placed closely above. This configuration is called a cathode lens (CL) and has been known since the beginnings of electron microscopy as the crucial component of the emission electron microscopes. As we already mentioned in Section I, Recknagel published the fundamental theory of this optical element as early as 1941 and showed that its basic aberrations are proportional to the ratio of the initial and final electron energies. The same should be expected for the reversed function in the SEM and this is indicated by Equation (41). More exact analytical relations for Cs and Cc for a combination of the cathode lens with the focusing magnetic objective lens with aberration coefficients Cf and Cfc were derived by Lenc and Mtillerovfi (1992b): l CS-k-~
E ( 'J~ 3 1)4 1 (k 1)2)3 1 + ~ (4~+1 v~§
+
\
2--v~
(42)
370
MULLEROVAAND FRANK / CC =
k3/2
( k - 1)2 {3~/kk- 1 1) 3 - K 2~/k
(43)
(~/--k+
with D as diameter of the anode bore. Instead of an abrupt potential transition in the electrode plane, the quadratic polynomial shape was considered here. For our simple characteristics of the energy dependences, development of Equations (42) and (43) into a power series for large k (i.e., small E) gives relations that are easier to grasp:
/
C s ~- -~p E +
Cc ~
(~
81
)
l E3/2
+ -i-~ Cfs E 3/~---
1 9 Cf E3/2 Ep E -+--~-fi}~ +... ~p
+
~ ~ ~
(44)
Equation (44) confirms the conclusions of the previous section: the immersion lens introduces the E 1 slope for both spherical and chromatic aberrations but eliminates the energy dependence of the focusing lens aberrations via the weight proportional to E 3/2. The same holds for the "aperture lens," i.e., the optical power of the CL field penetrating the anode bore and forming a divergent lens, as we will discuss below. If we now substitute Equations (42) and (43) into Equation (36), then into Equation (38), and finally calculate again the optimum aperture Otopt, we obtain the results shown in Figure 23. (In this section we complete the sets of model parameters, FEG SEM and TEG SEM, with D = 3.5 mm, E p = 15 keV, and l = 1.5 and 15 mm.) We see that the optimum angular aperture in the specimen plane is, at least at lowest energies, proportional to E -1/4. When substituting this into all four contributions to the spot size (Equation (36)), we get both da and ds proportional to E 1/4 while both dc and dD scale as E -1/4 and this can also be expected for dp. Because previously we found that these basic proportionalities are the same for both summation rules, with Equation (38) simply providing 1.6 times larger aperture and 1.8 times smaller spotsize, we used here only one rule. It is important to note that the optimum angular aperture just below the focusing lens, i.e., the beam aperture ac formed by the microscope column, remains nearly the same when switching the cathode lens on. Hence the SLEEM mode does not require any significant realignments of the column. In Figure 24 we see again a comparison of the calculated ultimate spotsizes, d~, for two sets of the SEM parameters as defined above; the summation rule (38) was used again. Obviously, the slope E -1/4 is actually achieved at low energies, namely in the energy range where the higher
S C A N N I N G LEEM
i
.
.
.
.
i
.
.
.
.
.
.
.
.
.
.
371
.
.
102 [ TE;.I~)="T:eFEG'-.1...... ~,""-.......
:
i----i
-o
: TEG~r . . . .
t_
E
101
10~
t ....
. . . . . . . . .
""~""'.ff..''""+22"".-...
, . . . . . . . . .
. :..;,,,:~.'~1-o
.-':~
i"
. . . . . . .
i
|
-
:
-"'""-
,=-
........
..~-.~:~
i
|
"
|
-
i_
. . . . . . . . . . . . . . . . . . . . .
|
|
,
i
,
,
i
.
,
|
,
,
,
i
,oo
energy [keY] FIGURE 23. The optimum angular aperture, ~opt, for the smallest spotsize, plotted versus electron energy for a CL-equipped SLEEM. T E G SEM and F E G SEM denote the two sets of SEM parameters given in the text; the summation rule (38) was used with Cs and Cc substituted from Equations (42) and (43), respectively. For the cathode lens mode, the aperture is shown both between the focusing and cathode lens ( - - 9 9) as well as in the specimen plane ( . . . . . . ); for the latter case the aperture without CL is also shown ( ). The numeric labels denote the maximum field within the CL in kV mm -1.
members in Equation (44) become negligible. For larger aberrations of the focusing lens this happens at lower energies so that, quite paradoxically, the overall drop in resolution between the primary beam energy and, say, 1 eV is smaller for the lower quality device--for the TEG SEM and 10 kV mm -], these spotsizes are identical in Figure 24. Figure 24 demonstrates one crucial fact: below some threshold of the order of hundreds of eV, even the routine microscope, equipped with the cathode lens, surpasses the top-quality device as regards the image resolution. This advantage is paid for by the fact that the specimen has to be immersed in the electrostatic field, the strength of which governs the spotsize. The optimum aperture varies with energy and is therefore not convenient to use when acquiring a series of micrographs typical for the SLEEM operation, i.e., showing the same field of view over a broader energy range. In this case some fixed angular aperture is adjusted and it is interesting to enquire how this modifies the resolution vs. energy curve. In Figure 25 we see that when fixed apertures are chosen from among those optimum for certain energy within the low-energy range, deterioration at higher energies
372
MOLLEROVA AND FRANK
9
"i.,,~
..
.
.
,,,
10 3
,
.
.
.
!
,
- ..~:, ,
,.-
~ ,
~ ",,,.
.
.
.
,
i
.
.
. . . . . . . .
: . . . . . . . . . . . . . . . . . . . . . ,
TEG
i
,
".
" . ~
.
,
,
~,
,
"~ 10 2 t,_._,
N
.m U~
O l
e~
i "----.i
01
if)
10 0 10 -3
10 -2
10 -1
10 0
101
energy [keV] FIGURE 24. The ultimate spotsize, de", for the optimum angular aperture Olopt, calculated for the two sets of SEM parameters denoted by TEG SEM and FEG SEM (see text) from the summation rule (38): the conventional SEM mode without CL (. . . . . ) and the SLEEM mode with the CL excited ( - - ) , namely for the maximum field strength labeled in kV mm -1.
9 . . i
.
.
.
.
.
.
.
.
~' 101 t"
..........
(I.)
1 2 ~ -
N o0
o Q. t,/)
10 0 I
10 -3
10-2
10 -1
10 0
101
energy [keV] FIGURE 25. The ultimate spotsize, dp m, for the optimum angular aperture ~opt, calculated for the model FEG SEM parameters (see text, maximum CL field 10 kV mm -1) from the summation rule (38) (. . . . . ), together with resolutions obtained for three fixed angular apertures, namely 1, 2, and 4 mrad ( - - ) .
SCANNING LEEM
magnetic
Ep
373
f
polepieceof OL
focusing lens
magnetic shielding
6-segment semicond. detector .. ._/~
____~__ __ ....
vl..1~
i
Ub
i
;:
specimen .I/
. . . . ~_
polepie~,~ ! ~Jens specimen
ofSPL "~==._ v////////////////a t~IPA ~\\\\\\\\\\\\\\\"~ -
"[~~~~/'
m
(a)
(b)
FIGURE 26. (a) Simplest configuration of SEM with the cathode lens introduced below the objective lens; (b) single-polepiece magnetic lens (SPL) installed below the specimen and serving as the focusing lens while the original objective lens is either switched off or used as an additional condenser lens (in the SLEEM mode, the anode/detector assembly was radially inserted from side to below OL).
is moderate only and, in some instances, a resolution really constant throughout the energy scale is obtained. In the previous paragraphs we concentrated on simple relations concerning the energy dependences of the beam aperture and spotsize. We assumed the electrostatic and magnetic fields of the immersion and focusing lenses as nonoverlapping and, furthermore, the shapes of electrodes and polepieces have not been taken into account. The simplest arrangement, shown in Figure 26(a), can be also realized via adaptation of a conventional SEM (Mtillerovfi and Frank, 1993), as will be mentioned below. An electrostatic focusing lens was used in LEEM by Liebel and Senftinger (1991) while Mtillerovfi and Lenc (1992b) applied to SLEEM the singlepolepiece magnetic lens (see Figure 26(b)). Khursheed (2002) compared the ultimate resolutions achievable in three configurations that included the specimen inserted into the magnetic field without any retarding, and both the nonoverlapping and overlapping magnetic focusing and electric retarding fields. Using a simple model of very thin electrodes and the bellshaped magnetic field (Glaser, 1952), he found that the overlapping fields provide 1.5 to 2 times smaller spotsize than the "sequential" configuration
374
MULLEROVA AND FRANK
and at 5 kV mm -1 a spotsize of about 1 nm for an electron energy of 200 eV was calculated.
D. The Pixel Size As we already mentioned in Section IV.D, the specimen response function for the total electron emission is composed of two bell-shaped contributions of different widths. The narrower peak corresponds to the SE1 part of SE, released directly with primary electrons, and its width is similar to the primary spotsize dp, amounting approximately to (d2+)~2s~)1/2, while the broader component is that of SE2 and BSE and its width is similar to the electron range R. At high energies, the SE and BSE signals are, as a rule, detected separately and the SE resolution is much higher than that of BSE. The SE2 contribution to the SE image is usually smeared so much that visually it is not apparent and when the resolution is measured between 25 and 75% of the signal rise on a sharp edge, the SE2 signal need not manifest itself at all. The BSE resolution is usually presented on small clusters of heavy metals so that the localization of information is improved by a sharp structure within the broad three-dimensional distribution of the BSE yield. However, at low energies the electron range approaches the escape depth of SE and the widths of both response functions become similar. As demonstrated for a silicon specimen by Reimer (1998), below 1 keV the SE distribution becomes even broader than that of BSE owing to lateral diffusion of SE2 after their release by BSE. In the SLEEM method, we usually detect a mixture of SE and BSE and use just the energy range where both distribution widths are comparable--this is why we have to consider the real resolution, or the pixel size, as determined by the full response function incorporating also the specimen. The problem was solved using the response function formalism by Frank (1996a,b). The spatial distribution IT(r) of the total emitted current in the surface plane can be written as
I T ( r ) / I p -- 8 C ( r ) +
r/(1 +/38)
f
r,)dr'
(45)
where Ip is the primary current. Let us assume both the column response C(r) and specimen response S(r) to be two-dimensional distributions of independent normal random variables. The normal distribution of BSE and SE2 (i.e., the shape of S(r)) was proved by Hasselbach and Rieke (1982) above 20 keV so at lower energies it can be assumed only as a rough
SCANNING LEEM
375
approximation and the same holds for the shape of C(r). One way of assessing the pixel size is to take the RMS distance of the emitted electron, dRms, which can be calculated for the axially symmetric case as
dRMS - - 2
[So-r2Ir(r) dr
/s0-1 ''' IT(r) dr
After substituting from Equation (45) Gaussians for both C(r) and S(r), we get dRMS
and
taking
(46)
two-dimensional
-- [8 -I- 0(1 -t- ,BS)l-'/218d 2 -I- 0(1 -I- flS)(d 2 -t- d2)] 1/2
(47)
where dp is the spotsize and ds is the RMS width of the specimen response. Equation (47) was then used for the estimation of the best achievable values of dRMS at low energies. The emission yields were calculated from the approximate relations reviewed above and the primary spotsize was assumed both for a standard SEM and for the CL-equipped one. The RMS specimen response ds was determined by M C simulations using software described by Czyzewski and Joy (1989) with the result
ds ~ CP-1E 1"75
(48)
where C - 9 x 10-ll kg m -2 eV-1. With the approximations described above, the pixel size dRMS exhibits a minimum (see Figure 27) enabling one to define the optimum imaging conditions for a particular specimen when the total electron emission is detected, as it is in most versions of SLEEM. Hence
"t"
,
,
'
'
I
'
'
!
. . . .
I
'
/ ~
//
10 2
//
TEG
nm +__
10 ~
f
f
f
f
f
~s
10 0 .
.
.
.
.
|
10 a
.
.
.
.
,
,
,
,I
104
Ep [eV]
FIGURE 27. Comparison of the primary spotsize ( - - ) with the total pixel size dgMs calculated for Cu (. . . . . ). The CL parameters were l = D = 5 mm and the summation rule (37) was used.
376
MOLLEROVA AND FRANK
optimum energies of the electron impact and ultimate values of dRMs were calculated for all three configurations indicated in Figure 27 and for the majority of chemical elements. The optimum energies move between 330 and 4530 eV while the ultimate resolutions were found as 5 to 13 times the nominal spotsize at 30 keV for both microscopes without CL and only 1.6 to 2 times for the CL-equipped model TEG SEM (Frank, 1996a). However, these data provide only broad guidance because of many simplifications made. The approach employing the specimen response function can be extended one step further, provided the SE emission is considered only (see Frank, 1996b). In the previous derivation we took the specimen to be fully homogeneous, with all yields constant with respect to r. Now we can progress to a specimen composed of a homogeneous substrate with a heterogeneous surface film or surface relief. Then, both r/and/~ in Equation (47) remain position independent but the emission distribution IsE (r) can be written as a convolution, Ise(r) = 6(r) | ise(r), with isE(r)/Ie = C(r) +
~[C(r) | S(r)]
(49)
which enables us to separate the imaged surface from the distribution of illumination by both PE and BSE. Because S(r) does not vary over the surface for a homogeneous substrate, we get the true specimen response function, which can be, for C(r) and S(r) approximated by Gaussians, written as ' R F -- G2(crp, r) + j3~(Z)G2 [ ( 4 + cr2)1/2, r]
(50)
where G2(ff, r)=(2rc)-lcr-2exp(-r2/2~2) is the two-dimensional Gaussian function. Equation (50) opens possibilities of using any acknowledged resolution criterion, like the Rayleigh one or those based on a certain encircled portion of signal, in addition to the evaluation via statistical moments that was performed before. In Figure 28 the real resolutions for C, Cu, and Au are compared for the Rayleigh criterion and the pixel size defined by 80 and 90% of the encircled signal. Obviously, the appearance of the resolution minimum, as in Figure 27, is connected with criteria oriented to the total signal (like dRMs) or to its major portion (like d9o). In the dR curves the minimum is not present at all and the dnn curves exhibit the minimum (connected with a significant influence of SE2) only for very high percentage nn. Already at nn = 80% the minimum disappears for the lightest element and at lower nn it is also not found. The above analysis showed that the real resolution has to be assessed by means of criteria oriented onto the central peak of the total response
SCANNING LEEM
101 ......
377
101 "in-;; - '/// I/. ... :". ..
......
~d~176
. . . . .
nm
nm
dR(C)
"
-0:c o,
dRo
- - - d.(Cu) ~ . -
d.(Au)
10 0
10 0 ~ .
. .|
. . . . . .
,
103
. . . .
!
,
.
.
. 1
104 Ep [eV]
"
.
.
,
i0 3
(a)
.
.
.
.
!
.
.
10 4 Ep [eV]
(b)
FIGURE 28. (a) Resolution dR calculated from IRF according to Equation (50) when the Rayleigh criterion is used (i.e., a drop of IRF to 36.74% of the maximum; see Born and Wolf, 1975) for three elements, with dRo representing the first term in Equation (50) only; (b) resolution dnn for nn= 80 and 90% of the signal encircled within the diameter defining the resolution, again with d,,,,ofor the first term in Equation (50). Parameters of the model FEG SEM and Equation (37) were used. function, i.e., criteria based on a certain decrease of I R F with respect to its maximum or on some encircled signal. These criteria show only a small extension of the pixel size with respect to the primary spotsize, as exemplified in Figure 28. On the contrary, the statistical moments of the signal distribution in the specimen plane overestimate the influence of species having diffused to great distances so that fully unrealistic figures appear at higher energies (see Figure 27). This indicates that even at low energies the conventional resolution tests can be used provided their evaluation respects the above-mentioned circumstances.
E. Spurious Effects The spurious effects influencing parameters of the electron probe in SEM are listed in Section II.C. Some of them are connected with the Coulomb forces acting between electrons moving within the beam so that the intensity of effects depends on the beam energy. The main phenomena include probe size broadening owing to stochastic e-e interactions, broadening of the energy spread (the Boersch effect), and defocus or probe shift caused by the overall space charge. The probe broadening caused by stochastic interactions was studied by Spehr (1985). He found the spotsize enlargement proportional to the normalized beam current
~: -- ~
I(Eo)
~-~
3/2
(51)
378
MULLEROVA AND FRANK
where I is the beam current, ot is the angle of beam convergence, I0 = 3.41 x 104 A, and E0 is the rest energy of an electron. This E -3/2 dependence is further enhanced by another factor that increases with decreasing energy with progressively varying slope and cannot be characterized by a simple proportion, but for short slow beams it approximately behaves as In 2 (const x E - l ) . Naturally, the final crossover at the specimen surface is the most critical one because the energy is lowest there. In cathode lenses, the beam aperture grows toward the specimen surface a s O/2(3( E -1 SO that altogether we get the probe-broadening rate somewhere around E -1. Mankos and Adler (2002) explored the problem of stochastic interactions for the cathode lens configurations. Using precise tracing of particle bunches through calculated electric and magnetic fields for both electrostatic and compound lenses with non-overlapping retarding and focusing parts, they obtained the "blur" values for wide ranges of the beam current and current density. Being oriented to direct imaging in the PEEM mode, their data range is shifted to larger currents and lower densities than those corresponding to the SLEEM situation. We can extrapolate their data to our case, the probe current of 5 pA and the spotsize of 10 nm at lowest energies, i.e., to the current density 5 x 103 mA cm -2, and obtain a broadening of about 1 to 2 nm. Otherwise, a linear increase in the blur with decreasing E~, was found. As regards the increase in the energy spread owing to e-e interactions, we already mentioned the fundamental work of Rose and Spehr (1980). For the stigmatic focus they calculated the extra energy spread to be (AE/E)= 2rcK (see Equation (51)) for low currents, so that AE~I1/2E1/4. This result is independent of the beam aperture ot provided ~c<< 1 and ol << 1-2E/Eo. The second condition is easily satisfied and for a beam current of 5 pA and aperture of 1 mrad, we get ~: ~ 2 x 10 -2 at 1 eV while for larger energies it further decreases as E -3/2. Thus, the Boersch effect is not enhanced at low energies. The average space charge within the whole beam acts as a divergent lens causing some defocus of the primary spot. Spehr (1985) showed that for a constant current density across the beam and ~c< 10 -2, refocusing of the appropriate lens enables the spot broadening to be corrected with negligible residual effect. For an electron beam with Gaussian cross-section, a contribution to the spherical aberration is generated too, with the corresponding confusion disc that, again for low currents, has a diameter de-e= 1.1~:D0, where Do is the diameter of the beam-limiting diaphragm. Nevertheless, at the same time it is claimed that this deviation can also be corrected by readjusting the lens excitations. The proportionality to ~c, i.e., to E -3/2, requires the effect to be listed here although there are no reports
SCANNING LEEM
379
about its practical demonstration so that successful correction via fine focusing can be believed. Important spurious effects in SEM are caused by the penetration of external electromagnetic waves into the column. These phenomena were reviewed by Frank and MfillerovS. (1999) and found negligible except the beam deflection 3y caused by a radial magnetic field Br, which amounts to 6y -- eBr (2Elm3) 1/2z"2 with ~ as the time of flight across the region exposed to the magnetic field. The beam trajectory inside magnetic lenses is shielded by magnetic circuits against the spurious fields relatively well so that the most exposed part is the trajectory along the working distance between the lower polepiece of the objective lens and the specimen. If this region is traversed by slow electrons at energy E, the time of flight is (1 + ~/k)/2 times longer than when electrons are decelerated to E from the primary energy Ee along the same trajectory. This means that the beam deflection is reduced (1 + ~/k)2/4 times, i.e., for example 266 • for k--1000. From this point of view, insertion of the cathode lens below the magnetic objective lens represents the optimum solution. Finally let us recall the problem of mechanical vibrations. This issue is common to all types of SEM and its impact simply depends on demagnification of the gun crossover. The most sensitive component to any vibrations is the cathode itself but in TEG SEM its movements are demagnified 103 to 104 times together with the crossover and become negligible. However, for FEG operated at room temperature the necessary demagnification remains of the order of units, so serious problems arise unless the device is carefully insulated from vibration sources. This problem is not specific to the SLEEM mode.
F. Testing the Resolution We have already mentioned that, even at low energies, the conventional tests of resolution, made with a specimen containing small particles of a heavy metal on a low-atomic-number substrate (most often gold on carbon), can be used provided their evaluation respects the signal composition of SE1, SE2, and BSE. For psychological reasons, it is desirable to extract from these tests numbers that approach very closely the calculated spotsize without any enlargement owing to diffusion inside the specimen. This means the tests should be performed solely upon the SE1 signal. In previous sections we showed that in the low-energy range where the lateral spread of SE2 and BSE emission shrinks and approaches that of SE1, progressively enhanced fraction of SE release takes place within )~esc and hence the SE1 signal relatively grows. It is reasonable to suppress the
380
MI21LLEROVA AND FRANK
distribution tail that appears in the edge width measurement by taking the thresholds far enough from the signal levels on adjacent facets; the proved algorithm is to measure between levels of 25 and 75% of the signal rise. Reimer (1998) used MC simulations to model the resolution test for emission distributions of all signals and also their integrals on one side of a moving straight edge and verified applicability of the 25/75 scheme. As we will discuss in the next section, the SE and BSE signals are detected together in the SLEEM mode and therefore extension of the lateral distribution of the total signal with respect to that of SE1 becomes even more probable. Nevertheless, practical experience showed that also here the 25/75 rule is suitable (see Figure 30). Another crucial circumstance, not taken into account with a conventional SEM, is the necessity of using a specimen that preserves a sufficient contrast throughout the full energy scale. It is believed that a difference in atomic numbers as large as that between Au and C should secure this. However, we see in Figures 13 and 16 that the signal yields already change their mutual relations drastically above 250 eV; other published data confirm this down to even lower energies, as Schmid et al. (1983) showed for eBSE. The contrast behavior of the standard Au/C specimen was verified in two instruments equipped with the same SLEEM detector and CL assembly described below. The microscopes differed mainly in the vacuum conditions; one had the usual medium vacuum (MV) of the order of 10 -4 Pa and the other used clean UHV at about 2 x 10-8 Pa. As shown in Figure 29, at 320 eV for both devices the Au/C contrast is substantially less than that at 3 keV but at 20 eV for the MV instrument the contrast fully disappears, while in UHV it is inverted and quite high. Surface contaminant layers being less transparent at 20 eV under worse vacuum might cause the difference but as yet the interpretation is not fully clear (see Mfillerovfi and Frank, 2003). Nevertheless, fine cracks are still apparent at the surface, the contrast of which is obviously due to enhanced electron absorption in deep cavities, and an appreciable signal rise at edges can be observed. Figure 30 shows a linescan across such an edge, taken at an electron energy of 10 eV, which demonstrates a resolution of 9.3 nm, to the authors' knowledge the best one achieved yet (Mfillerovfi and Frank, 2002). This value corresponds to the objective lens aberrations C s = 3 3 mm, C c - - 1 5 mm, published by Takashima (1994) for the working distance (WD) of 6.5 mm, and to W D = 8 mm used by us, which is larger than that appropriate for the guaranteed instrument resolution (1 nm at 15 keV). As regards the UHV SLEEM, the same measurement gave 11.5 nm at 10 keV and 26 nm at 10 eV.
SCANNING LEEM
381
FIGURE 29. Micrographs of the standard resolution-testing specimen with Au particles on a carbon substrate, taken (from the top) at 3020, 320, and 20 eV. Left column: dedicated UHV SLEEM of ISI Brno, right column: JEOL 6700F adapted for SLEEM. The width of the field of view is 100 ~tm (top left) and 200 lam (top right). (Reprinted with permission from Mtillerov/t and Frank, 2003.)
VI. DETECTION AND SPECIMEN-RELATED ISSUES
This review concentrates on SEM modes employing primary beam retardation close to the specimen. In the majority of instances the retarding field is also traversed by the signal electrons in the opposite direction so that these are accelerated and, if the field has its axial component strongly
382
MOLLEROV]k AND FRANK J
,
,
,
,
.
.
.
.
,
.
.
.
.
i
.
.
.
.
,
.
.
.
.
,
.
.
75%
.
.
.
.
i
.
.
.
.
i
.
.
.
100
.
i
.
.
.
.
.
,
.
.
.
.
,
.
.
.
.
.
.
.
i
.
.
.
.
,
,
,
,
~ A
.........
0
.
i
.
.
.
200
.....
.
i
.
.
.
.
\
i
1
.
.
.
i
300
.
i
i
i
i
l
i
.
.
.
400 nm
FIGURE30. Linescan acrossanedgein a micrograph ofthe Au/C specimen, taken a t a n energy of 10 eV (JEOL 6700F adapted ~ r the SLEEM method), with the edge width indicated.
prevailing, also collimated toward the axis. In the cathode lens configurations the specimen itself becomes one electrode of the electron optical system. These facts have a decisive impact on the choice of detection principles to be used. First of all, the classical Everhart-Thornley detector, extracting slow SE by a lateral electric field, cannot be used because the emitted electrons are being accelerated along the axis and also because the slow primary beam could be undesirably affected. Hence the objective lens with its focusing and retarding parts has to be considered together with the detector. Further, owing to acceleration of signal electrons, the crucial difference between typical SE and BSE energies is shifted so that usually both appear in the same order of magnitude. Then, separate detection of SE and BSE via conventional methods is not efficient any more and novel detection principles are needed. Finally, the specimen surface parameters, the roughness in particular, have to be considered for the cathode lens assemblies.
A. Detection Strategies In previous sections we frequently compared the properties of the immersion objective lens (IOL) in its general form with the particular case for w =0, in which the retarding part is called the cathode lens. It is worth continuing this also here: as demonstrated in Figure 31, the formation of the "signal beam" is significantly different in these cases.
SCANNING LEEM
383
FIGURE 31. Trajectories of electrons in the electrostatic immersion lens (a) and cathode lens (b); the potential difference within the lens is 10 kV; energies of electron emission are 5 eV (bottom half of the bundles) and 200 eV. The simulation was made using the SIMION 3D package (Dahl, 1995). (Reprinted with permission from Miillerov~tand Frank, 1999.)
For the IOL in the low-energy range, a non-negligible part of BSE impinge on the first electrode and can be detected in this plane while the SE emission is concentrated to a bundle that is focused into some crossover and then again spreads. This formation of an image of the emitting pixel is further supported by the focusing part of the IOL. Thus, the SE beam can be acquired even around the axis in a suitable plane above the IOL with a detector type normally used for BSE. The arrangement (see Figure 22) is then similar to the so-called "upper" SE detector utilized for acquisition of the SE beam from a specimen immersed in the magnetic field of the objective lens, which collimates the SE emission toward flux lines of the field (see Kruit and Lenc, 1992). Here the SE beam is already accelerated so that its detection is easier. The upper SE detector is usually situated above the deflection stage so that its action also influences the trajectories of signal electrons and a general issue here is to minimize or avoid escape of signal through the detector bore. We will discuss this problem further in the next sections (see Figures 40 and 46). If a CL is used (Figure 3 l(b)), the signal electrons are collimated to a diverging beam the width of which depends on emission energy and CL parameters. If we solve the classical equation of motion for an electron emitted with initial energy Ee under an angle | with respect to the surface normal into the CL field within which it is accelerated to energy E,,, we get for its radial coordinate ra at the end of field, i.e., in the anode plane, 2l sin|
[t e-sin2 t --COS] 1/2
384
MLTLLEROVA AND FRANK
where ke= Ep/Ee is the immersion ratio for the emitted electron, defined analogously to k. The entire emitted bundle for | is then concentrated into the spot of radius 21
ra'max = The
angle
of passage through
--l~/K/Z e----~ "
the
anode
(53)
plane,
O/a,
is given as
sinota=ke-1/2sin| so that the angular aperture of the bundle is Ota,max=arcsin (ke-1/2). W h e n drawing a ray backward from the anode plane, we find it crossing the optic axis, according to its emission angle, between l and l(kl/2-1)/(kl/2+ 1) behind the cathode, with the latter position corresponding to the paraxial ray. This virtual source is further imaged by the aperture lens in the anode plane and by the focusing part of the IOL. For secondary electrons with characteristic energy 3 eV (see Section IV.D) and for typical values of l = 7 mm and Ep = 15 keV, we get ra,max--0.2 mm and Ola,max~- 14 mrad. The beam of backscattered electrons is formed according to the BSE energy, which is dependent on the landing energy of the primary beam, but at very low energies similar figures are obtained to those for SE. Obviously, the detection made below the focusing lens has to be extended up to the close vicinity of the optic axis or again the throughthe-lens principle has to be incorporated. The previous simple considerations indicate a general problem: we have a narrow signal beam along the axis, escaping at least partially the detection through the central bore left for the primary beam. The signal losses can be reduced if the signal beam can be again broadened within a suitably arranged electric field as is done in the EDOL-type lens already mentioned; we will return to this arrangement in the next section. The issue can be fully solved via deflection by means of crossed electric and magnetic fields, i.e., by a so-called Wien filter or E x B filter (see Figure 32). The electric and magnetic forces subtract for the primary beam direction, but for the opposite signal beam direction they add and cause its deflection toward the detector. The Wien condition for equality of electric and magnetic forces can be easily fulfilled for the homogeneous parts of the fields but it is more difficult to satisfy for the spurious fields at the margins of electrodes/polepieces. In addition, any spread in electron velocities causes beam dispersion. This is why two identical but oppositely oriented filters are often incorporated so that the primary beam passes both and any undesired modifications are mutually compensated while the signal beam escapes between the filters (see Figure 46). In order to further minimize any influence on the primary beam, the Wien filters can be made
SCANNING LEEM
385
:Z
aaee 'or ~FapFE
.
.', ........
F
........
FIGURE 32. Principle of the beam deflector employing crossed electric and magnetic fields.
weak, just sufficient to deflect the signal beam to where it can enter some other electric field, not penetrating to the optic axis, that extracts it strongly towards the detector; for example, see Figure 33 and the same principle is shown in Figure 46. Various modifications of detector assemblies containing Wien filters have appeared in the literature since the 1980s (e.g., Schmid and Brunner, 1986; Brunner and Schmid, 1987; Reimer and Kissens, 1994; McKernan, 1998). Zach and Rose (1986) studied the influence on the primary beam of filter aberrations and proposed using higher order than dipole fields. A detailed study of the filter properties, including fringing fields, was presented by Kato and Tsuno (1990). A significant effort has also been invested in shifting the range of efficient operation of BSE detectors down to lower energies, i.e., in breaking as much as possible the traditional threshold at 2 to 3 keV. The amendments include both technological improvements concerning the preparation of scintillator surfaces and the introduction of extraction fields in such a way that secondary electrons are still not incorporated. Important studies include those of, for example, Autrata and Hejna (1991), Autrata et al. (1992), Hejna (1994), Autrata and Schauer (1994) and Hejna (1998). New detector principles have emerged that employ sophisticated arrangements of electric fields, created by electrodes situated within the magnetic lens bore and gap, and permitting a wide range of manipulations with the emitted electrons and extension of the scope of operation modes of the upper SE detector. These operation modes include collimation of the SE beam for enhanced detection efficiency, reflection of a portion
386
MULLEROVA AND FRANK
- - - - - - - - - - x(z) .... y(z)
/f,
j"l
.........
!
/
prima~;r
iI i
~ ~ ,~
9
L(L(L~
*
.......
~es '
"~
[magnetic .... i saddlecoils 1] / magn"circuit / ,
9
.
I
|
9
,
9
,
.
.
1 cm
~ ,
I
9
I! I
1///
upperstage 9
'
i///
9
|
|
i
.
.
.
.
I magnetic I saddlecoils l] magn"circuit ]
lowerstage
' i
,
,
,
,
I_l
I
i
i
,
,
,
i
I
,
9
9
,
i
,
,
,
,
FIGURE 33. Scheme of the double Wien filter with intermediate electrostatic mirror for deflection of the signal beam in an SEM. The bundle of SE trajectories is shown for the emission energy of 4 eV and emission angles within + 70~ Ub = - 10 kV. (Reprinted with permission from Pejchl et al., 1994.)
of the SE in order to achieve the charge balance at a nonconductive surface without charging, and, in combination with a moderate specimen bias, conversion of accelerated SE, impacting a converter surface, to tertiary electrons that are detected normally. In this way, good-quality micrographs were obtained down to 100 eV (Kazumori, 2002). An analogous configuration of electrodes, combined with the E • B filter, enables one to control the content of SE and BSE in their mixture detected by a single (upper) detector. In this configuration, BSE are converted to SE and biases of the electrodes can discriminate between SE from the specimen and those from the converter surface. These combinations with the crossed E • B fields appeared for the first time in the early 1990s (see Sato et al., 1993). Inevitably, arrangements of all electrodes are being published only schematically because details are considered confidential. Nevertheless, the CAD systems available do enable one to tailor the above-specimen fields in various ways and to optimize the detection efficiency for individual portions of the energy and angular distributions of total electron emission.
SCANNING LEEM
387
B. Detectors
In the previous section we listed the possible approaches to detection of electrons in systems with retarding field elements. Now we will describe several actual configurations. For IOL setups, i.e., with the retarding field not directly applied to the specimen, the variety of detector assemblies is very broad. For SE detection, they mostly rely upon the through-the-lens principle and detect SE either with a coaxial scintillator-type detector or deflect them by an E x B element toward a side-attached detector similar to the ET type. As regards BSE detection, conventional assemblies below the IOL polepiece are utilized but novel approaches have also appeared that include conversion of BSE to SE and detection of a controllable mixture of SE and BSE as mentioned above. Let us recall here the simple EDOL arrangement published by Zach and Rose (1988) (see Figure 34(a)), in which an accelerating electrostatic lens is employed and designed so that the conical electrodes generate significant radial components of the field. Within the first accelerating part of the lens, the SE emission is collimated to a beam while in the decelerating part the beam is, owing to radial forces, appropriately broadened so that it hits the annular detector with a reasonably large central bore. In a configuration according to Figure 34(b), the decelerating part of an electrostatic lens is similarly utilized to broaden the beam but here the lens is of the decelerating type and hence its first part is employed for this purpose. A further difference consists in using the conical electrode as the electron converter transforming accelerated signal electrons to tertiary electrons that are directed by the radial field toward a microchannel plate (MCP)-based detection assembly (Frank et al., 2000a). In this setup, the collection efficiency for 10 eV signal electrons, i.e., the probability of their impact on the converter surface, was calculated to exceed 98% and, after conversion and passing the MCP, 35% of emitted electrons still create signal impulses. A setup on this principle, an electrostatic detector lens (EDL), can be more widely utilized as it enables one to introduce a segmented or even twodimensional collector below the MCP and to acquire data about the angular distribution of emission. For completeness, let us also recall the MEDOL configuration (Figure 22) in which the signal beam is projected onto the detector by the combined action of both components of the compound lens. Now we will specifically deal with detection in systems that employ a cathode lens, particularly those based on adaptation of a conventional SEM. The authors' first experimental arrangement contained the detector assembly shown in Figure 35(a) (Mfillerov~t and Frank, 1993) in which, on the surfaces of the diaphragm and lower polepiece of the objective lens (OL),
388
MOLLEROV,~t AND FRANK
Conv SE traje
~
0 v (8 keV)
annular detector /
7 kV (15 keV)
CPI
7.5 kV (500 eV)
CPO Coil
_
Sp
, / / ~ specimen --- 20 mm --~
(a)
(b)
FIGURE 34. (a) Scheme of the EDOL arrangement with an accelerating lens that broadens the signal beam inside its decelerating second part (electrode potentials are shown together with electron energy in parentheses). (Reprinted with permission from Zach and Rose, 1988.) (b) Similar principle combined with a converter of accelerated signal electrons into tertiary electrons detected by a multichannel-plate-based assembly (L, lens; Conv, convertor; CPI and CPO, input and output of MCP, respectively, Coll, collector; A, anode; Sp, specimen). (Reprinted with permission from Frank et al., 2000a.)
the accelerated signal electrons are converted to tertiary electrons and these are attracted to a conventional ET detector with the front grid removed in order to allow the scintillator field to penetrate towards the axis, as shown in Figure 35(b). The advantages of this type include very low price and easy realization but the drawback is the quite large working distance that is necessary. In fact, the same arrangement was introduced by manufacturers in the form of the upper detector with converter (see above), but for an easy adaptation in users' laboratories the space above the SEM objective lens was, of course, not accessible. Another successful design employed the single-polepiece magnetic lens situated below the specimen (see Figure 26(b)), now completed with the anode of a CL and a BSE detector with a YAG crystal; the scheme of the assembly is shown in Figure 36. In this setup, a micrograph with a resolution of 80 nm at 0.5 eV electron energy was obtained for the first time (Mfillerovfi and Lenc, 1992b). This type is hardly suitable for adaptation of classical SEM instruments but was used, for example in a specialized lowenergy SEM for inspection of semiconductor structures at a landing energy of 800 eV and a primary energy of 20 keV (Meisburger et al., 1992). The most successful arrangement to date is shown in Figure 37. A crucial component is the YAG:Ce 3+ single-crystal scintillator disc with small central bore of depth and diameter 300 pm, side-attached to a light guide
SCANNING LEEM
~
oPOlepiece of OL
~~176
anode ~
assembly
~
~
~
~t~ " Y ' ~
.... ~
I
' i
,.=.~I
]I ' ' ,
/
/
~
/
/
i L. . . . . . . . . . . /
OL
ETdetector
I I-t[-l\,c m .............. t l l l a t o r -A--
,n
0.1V
~____a~:~ .... 9 ~
Ub _ =__..a
~"
389
.....
,t
1V lOV lOOV
lOOOYl
.... ~ ~ \ ~ _ _ _ _ J anode of CL
§ ~+lOkV
\ specimen
J I
sc~tillator
~'
insulator
FIGURE 35. Configuration of the SLEEM mode detector utilizing conversion of accelerated signal electrons on surfaces of the diaphragm and lower polepiece of an OL, and extraction of tertiary electrons toward a conventional ET detector (left); equipotential surfaces within the assembly when the front grid of the ET detector is removed (right). (Reprinted with permission from Frank and Mfillerovfi, 1999.)
OL p o l e ~
light-guide
/~
~ ~
9 9 elmag. shielding
in-lens deflection coils anode of CL specimen
i>/' single polepiece lens
[,,
9
p
I ~
FIGURE 36. A combination of the cathode lens with a single-polepiece lens situated below the specimen.
390
MOLLEROVA AND FRANK
~JE PRIMARY
LECTRONS
~E
DIAPHRAGM ANODE
DETECTOR CATHODE/ LENS
Ub
SPECIMEN
INSULATOR
FIGURE 37. The CL/detector assembly with a YAG:Ce 3+ single-crystal scintillator. (Reprinted with permission from Frank and Mfillerovfi, 1999.)
made of organic glass (for standard vacuum applications) or of quartz (for bakeable UHV instruments). The bore size was tuned to some balance between reasonable dimensions of the field of view and successful acquisition of very-low-energy electrons collimated towards the close vicinity of the axis. As shown in Figure 38, for one typical set of dimensions (used in the experiment described in Section VIII.E) and for normal impact of PE, signal electrons are detected above 0.5 eV of emission energy. This configuration is similar to the so-called Autrata-type BSE detector (Autrata, 1989) but important differences are the much smaller central bore and the related necessity for fine adjustment of the crystal position in all three axes. Fortunately, this adjustment is decisively facilitated by the fact that the upper crystal surface is also active so that the detector bore is directly observed on the SEM screen (see Section VII.C). The bore shape with a 45 ~ sink is dictated by several issues that include requirements of the boring technology, feasibility of a conductive coating of the inner bore wall, and an advantageous axial field distribution. It is obvious from Equation (42) that one term in the relation for Cs, namely aberration of the anode field, is inversely proportional to the bore diameter D and hence D should not be made too small.
SCANNING LEEM
(~)m [deg] 80
I
.
.
.
.
I
"
'
'
'
391
'
I
'
"
'
"
60 40 20 i
10 "1
i
I
i
,
,
10 o
.
I
101 Ee[eV]
102
FIGURE 38. The maximum emission angle, l~)m, of an electron with the emission energy Ee for which the electron still escapes through the central bore. Solid line: data calculated from Equation (52) for ra=0.15 mm, l = 11 mm, E~,= 10 keV; squares: exact values obtained via trajectory simulations using a software described by Lencovfi and Wisselink (1990). (Reprinted with permission from Frank et al., 1999.).
'7,
j
.... ; .......
E2
0
2
4
z [mm]
6
8
10
FIGURE 39. Derivative O~/Oz of the axial potential distribution (I,(z) for the three anode shapes outlined in the inset (calculated using software described by Lencovfi and Wisselink, 1990).
The shape shown in Figure 37 produces the axial potential distribution that resembles more closely the distribution corresponding to the outer diameter of the sink than that of the inner one (Zoba6ov/t et al., 2003); see Figure 39.
392
MOLLEROVA AND F R A N K
upper SE detector
scanning
coils
! V//////'/////A
OL
,i__~'W~N~ ~] ] ~////////~ a n o d e specimen I i
FIGURE 40. Scheme of trajectories of primary and signal electrons in a CL-equipped SEM with an upper detector.
With regard to adaptations of commercial SEMs to the SLEEM method, we should also mention an alternative employment of the upper SE detector, either in a coaxial arrangement or side-attached one with the electron converter, when it is combined with a CL operated between the specimen and the lower polepiece of the OL. Here we gain the space required for the detector as in Figure 37, so that a shorter working distance can be attained. In Figure 40, a sketch of electron trajectories is shown for the case when none of the above-mentioned additional electric fields for manipulation with signal electrons is considered. All previously described setups are intended for adaptation of conventional SEMs that naturally have their full columns at the ground potential and hence any retarding field can be created only via a specimen bias. This can impose serious difficulties particularly for instruments equipped with an air-lock for insertion of a specimen cartridge. But in any case the specimen biasing loads the routine operation with extra tasks and checks. It is much more convenient to use the booster principle with a positively biased central tube that creates the necessary retarding field even toward the specimen at ground potential--the next section will address these questions. Here again we should recall the family of IC testers in which CL/detector assemblies are increasingly used and designed subject to an extra requirement that is not so important for other SEM applications, namely
SCANNING LEEM
393
that the beam current be as high as possible in order to achieve a high throughput in the productions checks (see Section VII.B).
C. Signal Composition Within the CL field the whole energy spectrum of emitted electrons, outlined in Figure 11, is accelerated by the potential difference between specimen and anode. For larger CL fields, the energies of the SE and BSE are of the same order of magnitude and no type of detector can efficiently separate them unless a true energy filter is incorporated. The particular composition of the signal mixture depends on parameters of the fields and on the geometry and here we can only show one typical example. Let us consider the CL/detector assembly according to Figure 37 with a YAG:Ce 3+ crystal for which Autrata and Schauer (1998) published the detection quantum efficiency (DQE), defined as the squared ratio of the signal-to-noise ratios (SNR) at the scintillator input and output. For a cosine distribution of both SE and BSE emissions, the portion of electrons hitting the scintillator (or the collection efficiency) is simply
P = IDET/I = sin2~max -- sin2Omin
(54)
where Oma x and (~)min correspond to the marginal rays incident onto the scintillator, which can be determined from Equation (52). Figure 41 shows P and DQE for both SE and BSE, plotted with respect to the landing energy of the PE together with the detection weight
WBSE/SE
--
PeSE DQEBsE PSE DQEsE "
(55)
This obviously favors BSE in a ratio between 5:3 and 4:3. Since the SE yield usually surpasses the BSE one, the signal mixture, governed by the weight WesE/SE, represents a more or less balanced combination of both components. The graph in Figure 41 depends on particular values of three parameters, Ep, D/1, and Do/l (Do being the outer scintillator diameter), but also for other reasonable combinations of these factors similar results for WeSE/SE are obtained. With below-the-lens detectors the BSE/SE ratio cannot be efficiently controlled and generally a sum of both signals is obtained. On the contrary, setups employing the upper detector open possibilities for controlling the signal ratio at least down to about 200 eV where SE and BSE cease to be
394
M[JLLEROV]i '
'
i
9
9
:
1
:
......... ~"
..'~" _~
~
9
FRANK
i ,
-#.
9
:
,
'
:
i
9
r
~
i
o__,_~___o . . . . .
...................
',
_._P~ ~ "~z ..... DnE "',
\/
-,.K,
--~ , ..... r
BSE
~
101
-"
..~
.-. .~. .. ~ .t . . > ~ . .,,
. . . .
9
,~,_-~, . . . . . . . 9 . . . . . . ,
',. . . . . . . . . . . . . . . . . .
. . . . . . .
w-
PSE
":'I-.-~
,
0
9
,
~. ~:._ ~ - b - - 4 - ~ . . . . . . . . r
0.5
AND
"
%
. . . . . . . .
10 2 emission energy,
10 3
10 4
Ee[eV]
FIGURE41. Collection efficiencyP for SE emitted at mean energy of 3 eV, for BSE emitted at 75% of the landing energy of PE (above 50 eV), and for eBSE below 50 eV, calculated for the assembly shown in Figure 37 with a crystal outer diameter 10 mm and bore diameter 0.3 mm and field length l= 7 mm, together with the DQE values corresponding to the various impact energies and with the weight W~SF4SEaccording to Equation (55).
distinguishable even in the energy spectrum of emission--see simulation results of K u h r and Fitting (1998).
D. Specimen Surface One important characteristic of an IOL is the magnitude of the electric field penetrating toward the specimen surface. For the CL as the extreme case, the surface field is the m a x i m u m retarding field used, while IOL arrangements with a nonzero working distance w, i.e., with the specimen electrically connected to the first electrode, are usually regarded as situating the specimen in a field-free space. Let us assess the field penetration outwards of the retarding lens for a simple case of flat electrodes of the same thickness t and identical bore diameter D, situated at distances w and w + l from the specimen, as in Figure 21. For three particular IOL geometries we show in Figure 42 the ratio of the surface axial field to the m a x i m u m axial field within the lens plotted versus w/l, together with the immersion ratio k for which the IOL alone focuses the beam onto the specimen surface. We see that for very low energies, i.e., say for k _> 500, the surface field does not drop below 10% of E z , m a x . Nevertheless, if a magnetic lens contributes to the probe focusing, the working distance further shortens. If both lenses are of an equal optical strength, the surface field is E z - 0.5Ez, max.
SCANNING LEEM
I
,
..~ 10 2
,
:
,
~
,
~
"
,
,
~,
~,
,
-.
' ,
! ,
~ :
~.
~
395
~' ~
,
,
,
,
",,.._b",~.a ~'--.~
"--.
',
:
01
10 0
10 -1 0
0.3
0.6
0.9
1.2
working distance, w/I FIGURE42. The axial field strength on the specimen surface referred to the maximumfield strength within an IOL, and the immersion ratio k for focusing the probe by the electrostatic lens only, plotted for three configurations of the IOL with flat thin electrodes: (a) D = l, t = 0; (b) D = l, t--0.1 l; (c) D = l/2, t--0.1 l (for symbols see text). Obviously, the field penetration has to be taken into account even for an IOL with a nonzero working distance. In order to improve the situation, the lens electrodes have to be shaped and their bores tuned to create an axial potential distribution falling as sharply as possible in the close vicinity of the specimen. For this task powerful simulation software packages are available; the optimization procedures were studied by Preikszas and Rose (1995). We will now address the specimen surface roughness. While no problems are expected and appear with an IOL, it has been repeatedly argued that a CL is unsuitable because the specimen surface has to be very smooth if not polished like that of an electrode. Practical experience shows that the real demands are not so strict albeit application of the method is without any doubts restricted to observation of flat specimens. Naturally, the m a x i m u m applicable field between specimen and anode is restricted by the danger of a possible discharge that increases with the specimen roughness. Also the imaging process alone requires that the CL field should be homogeneous up to the very specimen, which can be so only for smooth surfaces. Tolerable roughness depends on shapes of protrusions and depressions and on the field strength. Any radial forces, connected with "waving" of equipotential surfaces above the surface relief, shift or smear the primary probe and locally deteriorate the image. Nevertheless, the above-specimen equipotentials do not simply copy the proper surface but depend also on the distribution of surface dipoles and any trapped charges.
396
MI21LLEROVA AND FRANK
FIGURE 43. Si (100) substrate with heterogeneously etched trenches of both width and depth 3 lam, with some traces of Cu decoration, imaged (from the left) at 5 keV, 250 eV, and 1 eV; primary beam energy= 10 keV, CL field -- 1.5 kV mm-1, width of the field of view= 20 ~tm. To the authors' knowledge, no study focusing on this issue has been published as yet. In Figure 43 we see one practical example of a specimen with known shape and dimensions of surface relief features and can verify that even in the 1 eV micrograph no traces of local deterioration at the trench edge are apparent. Other similar experiments also resulted in the conclusion that a surface relief up to a p - p height of a few ~tm could be tolerated for the SLEEM mode at moderate CL field strengths not exceeding 2 to 3 kV mm -1. Otherwise, in Figure 43 we can also notice a strong shortening of the depth of focus with decreasing electron energy. Restriction to a relief not exceeding a few gm is more or less in accordance with the depth of focus, which is here significantly shortened, owing to enlargement of the beam aperture within the CL by approximately ~/k times. Otherwise, limitation to the depth of focus is felt to be the most important disadvantage of the method and can be at least partly suppressed only at the cost of resolution, as indicated in Figure 25. Finally we recall one more of the traditional misgivings regarding the S L E E M / L E E M methods, namely that UHV conditions and atomic cleanliness of the surface are unavoidable because of extreme surface sensitivity. It is true that at around 50 eV of landing energy, where the minimum penetration depth of PE is achieved, the surface sensitivity is high and the image contrast is dominated by that of surface contaminants. However, above and particularly below this threshold the electron penetration grows steeply so that at a few eV it is comparable to that at tens of keV. This means that the method itself does not put any demands on the surface cleanliness but such demands might follow from phenomena to
SCANNING LEEM
397
be observed. For example, phenomena connected with surface crystallinity, reconstructions, phase transformations, etc., can take place solely on surfaces free of amorphous contaminants that might prevent atoms arranging according to the distribution of forces inherent in the crystal.
E. Specimen Tilt
When the specimen is not immersed in an electric field, normal conditions for the specimen tilting can be expected irrespectively of whether the retarding field is used or not. When only a weak field penetrates the anode bore toward the specimen, some balance has to be sought between the image shift and deterioration on one side and the tilt angle on the other side. In the CL any specimen tilt introduces a lateral field component that is not considered in the simple electron-optical theory outlined above. Small specimen tilt can be easily caused by imperfect fixing or sticking of the specimen to the holder so it is advantageous to have the specimen stage equipped with the double-tilt facility at least within a small range. However, it is also interesting to explore the limits of an intentional tilt introduced in order to get the primary beam incident under an angle. Let us now look at the consequences of a moderate tilt at an angle co. Having the anode of the CL in the plane z = 0 at potential 9 = 0 and the cathode at z = 1 and 9 = ~0, we get now the CL field, for the tilt made with respect to the y axis, modified to z
9 (x, z) - - ~ 0 l + x tanw"
(56)
A solution of the equations of electron motion in this field was presented by Frank et al. (1999). The lateral component of the CL field causes some shift A of the primary spot in the tilt direction. For small values of co this shift amounts to 2
a -5~
(v/-k - 1) 3
(k_l)2 ,
(57)
i.e., for very large k it tends to (2/3)co/. This magnitude of shift is quite significant so that when tilting the specimen intentionally, we have to do it in very small steps and to correct the position of the field of view in between. A further effect of the tilt is a unidirectional smearing of the primary spot owing to the lateral field created. In scanning devices, it is reasonable to express the image resolution via the number N of spotsizes filling the field of
398
MOLLEROV.dt AND FRANK
view and to compare this figure with the number of pixels acquired. Naturally, the optimum operation mode is achieved when these two numbers are equal. Normally, the spotsize and the size of the field of view are to a first approximation independent so that the optimum mode for a given number of pixels can be adjusted via the magnification. Nevertheless, imaging with some excess nonutilized information or with insufficient information density is also available for the magnification below or above the optimum, respectively. In other words, the number of spotsizes within the field of view is inversely proportional to magnification, and for any number of pixels acquired some optimum size of the field of view exists. In our case the beam inclination, generated by deflection coils in order to reach an off-axis pixel, plays its role in the spotsize deformation so that the optimum number of pixels N directly results from the configuration data as 3
N
TM
(7~/_~_ lO)otcW"
(58)
This number corresponds to the margin of the field of view while toward the optic axis the spotsize linearly diminishes toward its original dimension for no tilt. When taking typical values for the very-low-energy range, i.e., say k = 1000 and ore-2 mrad, and considering 1~ tilt, we get N = 407, i.e., a number on the edge of acceptability. An additional consequence of the tilt is the oblique impact of the primary beam, which is deflected by the lateral field component. Notice that this change in the impact angle is homogeneous within the field of view and has nothing in common with inclination due to beam rocking around the pivot point of the scanning system. For a certain deceleration, defined by a value of k, we get some tilt angle COmax for which the illumination becomes glancing: ~, (.Omax-
1 / 3 ( k - 1) k V
2
(59)
Independence of O)ma x on any other parameter offers an advantageous possibility of calibrating the true tilt scale according to the specimen bias causing a near-glancing impact easily recognized from long shadows of relief details. Otherwise, the impact angle can be assessed from Figure 44; this plot depends solely on Ee, which is here 10 keV. Obviously, the impact angle is, except in the near-glancing situation, well approximated by cok 1/2. Even very small tilts of tenths of a degree can at very low energies secure a full scale of impact angles, which is important for applications connected with the acquisition of the diffraction or energy-band contrasts.
SCANNING LEEM .
.
.
.
.
.
.
399
I
.
.
.
.
!
'
80
.'o
60
,
m 40
10 -1
10 0
101
10 2
landing energy, E [eV] FIGURE 44. Dependence of the beam impact angle on the landing energy for the specimen tilt angles shown (Ep= 10 keV); exact values are shown together with those approximated by o~k1/2. (Reprinted with permission from Frank et al., 1999.)
The above analysis showed that even with the CL the specimen can be tilted sufficiently to observe phenomena or features that require a tilt for this purpose. Moreover, the mechanical tilts necessary for large impact angles of the beam are only tolerably destructive as regards the image quality.
VII. INSTRUMENTS
A. Adaptation of Conventional SEMs As noted in the introduction, many attempts to design and build a SEM incorporating the retarding principle have been performed and the majority of them can be classified as adaptations of conventional instruments. Mfillerovfi and Lenc (1992a) reviewed the older works and we will not repeat here this literature survey. This section will discuss some recently applied approaches without aiming at a complete summary of relevant publications. It is obvious that in a conventional SEM the way of providing beam deceleration in front of the specimen is usually restricted to specimen biasing to a high negative potential. An additional electrode, placed above the specimen and electrically connected to it, enables one to arrange for a nonzero working distance of an IOL while without such an electrode we get
400
MULLEROV.~ AND FRANK
the CL. The latter alternative has proved itself successful in all groups of application tasks listed below in Section VIII and experience has been collected from adapting microscopes of all major manufacturers. After gaining preliminary experience with the configuration shown in Figure 35, the setup of Figure 37 was repeatedly installed because of its shorter working distance, easy alignment, and superior efficiency of the signal collection, albeit at a significantly higher price. Up to now, in all versions the YAG:Ce 3+ single-crystal scintillators were used with a thickness of 2 or 2.5 mm and outer diameter between 10 and 20 ram. The light-guide shape is partly dictated by the arrangement of the OL polepiece and of the x - y stage but otherwise some space exists for optimizing the shape with respect to the light transfer from scintillator to the side-attached light guide (see Schauer and Autrata, 1998). It is recommended to make the detector retractable so that the resulting restriction to the field of view is not preserved for other operation modes. It is sufficient to provide specimen insulation for about 15 keV while for practical microscopy 10 keV of primary energy is most suitable. In this case the overall working distance should be not less than 8 mm from which 5 mm is left for the CL field. In SEM instruments without specimen loading via an air-lock, it is usually easy to design an insulating insert cup into the standard specimen cartridge so that the specimen holder connects to a high-voltage contact via a pin passing along the stage axis. This design leaves intact all specimen movements including rotation. In air-locks the specimen cartridge is usually side inserted so that some additional mechanism is needed for contacting from the lower side of the specimen already loaded. Alternatively, the contact can be connected in the direction of the specimen loading and a flexible cable used between the specimen stage and feedthrough. These designs have to be tailored to a particular instrument and to its full setup with all options and attachments. The specimen biasing itself needs a negative supply with a ripple not exceeding 10-5 of the output voltage, finely adjustable in steps of 1 eV or smaller. Because the supply is usually operated near its maximum output voltage, the parameters should be assessed for the full scale. Generating the low landing energy of electrons via the difference between two high voltages is obviously not an optimum solution not only because of the addition of instabilities of the two supplies; it would be more advantageous to apply a voltage directly between the gun cathode and specimen. However, for CL applications this supply would have to be designed as passing smoothly through the zero voltage to the opposite polarity, e.g., during alignment, which is a feature not available with commercial laboratory supplies. The alternative and better solution consisting in using the beam booster (an insulated and positively biased tube around the optical axis between the
SCANNING LEEM
"booster". , insulator ~ magnetic ~ . ") objective ~I lens
401
,,o+ U
"I > >
\xi
-\
\
\
\
specimen
\
\
N
,
I
I/'/
~
I
/
/
/
/
/
/
/
I
,/
/
9
/
/
FIGURE 45. Possible design of a booster inserted into a magnetic pinhole lens. (Adapted with permission from Beck et al., 1995.)
gun anode and bottom of OL, see Figure 45) is mostly reserved for dedicated instruments but adaptation of this type to a conventional SEM was also reported (Plies et al., 1998). Let us explicitly state an obvious fact that with a commercial SEM containing the booster, the adaptation to the CL mode might be restricted to mere removal of the final electrode of the IOL or to its connection to the upper electrode; in this way the retarding field is shifted to between the end of the booster and specimen.
B. Dedicated Equipment
To the authors' knowledge, among general purpose SEM instruments marketed at present no IOL-containing dedicated device exists except the 1500 Series SEM of LEO Electron Microscopy with the Gemini lens shown in Figure 22 (see http://www.leo-usa.com). The new type of JSM-7400F of JEOL already incorporates specimen biasing but only to 1 to 2 kV and the purpose is declared to consist solely in acceleration of SE toward an electron converter where they are transformed to tertiary electrons detected by the upper detector (Kazumori, 2002). Probably all recent IC testers, i.e., specialized SEMs with very high beam current and a scope of operation modes tailored to inspection of semiconductor structures, including measurement of critical dimensions and local voltages, generation and sensing the electron-beam-induced currents, and operation with surface charges compensated by controlled
402
MOLLEROVA AND FRANK
Schottky cathode i
anode
i
SPCL
diaphragm
0=41=0
VVien filter 1
-
"~j
I
upper S E detector
I SPIOL
W i e n filter 2
scanning coils "''""
j lower SE detector
FIGURE 46. High-probe-current, low-energy SEM column equipped with a single-pole condenser lens (SPCL) and a single-pole objective lens (SPIOL) (see text for details). (Reprinted with permission from Beck et al., 1995.)
back-streaming of SE, are solved with immersion objective lenses (see, e.g., Meisburger et al., 1992; Miyoshi et al., 1999). Let us describe two of these solutions in more details. Beck et al. (1995) summarized problems connected with the formation of high-current low-energy probes and designed the dedicated column shown in Figure 46. It incorporates the central booster at + 9 kV (consisting of the gun anode and electrodes 1 to 4) so that with the Schottky cathode at - 1 kV and specimen at ground, the primary beam is held at 10 keV throughout the column but within the CL is retarded to the final 1 keV. Using singlepolepiece configurations both as the condenser lens (Cs= 13.2 mm, C c = 11.5 mm) and objective lens ( C s = 1.05 mm and Cc=0.83 eV at a
SCANNING LEEM
403
working distance of 8 mm and focal length 5 mm, when the retarding field is taken into account), they reached the calculated spotsize of 46 nm and the measured resolution of 50 nm. The beam current was calculated to reach 150 nA but measured only 20 nA, which was ascribed to insufficient vacuum conditions in the gun chamber. The lower SE detector was used only with an unbiased booster while in the low-energy mode the accelerated SE are deflected in the lower Wien filter to outside electrode 2 so that they can impinge on the upper SE detector. Although the Wien filter did not deflect the primary beam, it caused dispersion, astigmatism, and some higher-order aberrations that required pre-compensation by the upper Wien filter with opposite orientation. Meisburger et al. (1992) used the primary beam at 20 keV in the column and decelerated it in front of the specimen held at -19.2 kV together with the nearest electrode of the immersion objective lens that was combined with a magnetic single-polepiece lens below the specimen. Again a resolution of 50 nm was achieved at the landing energy of 800 eV with 50 nA in the probe. As above, two Wien filters were incorporated of which the lower one deflected signal electrons to a semiconductor detector with a fiber-optic light guide while the upper Wien filter incorporated in its electrostatic octupole the blanking unit, stigmator, and centering system. More instruments of the type described above can be found at major producers of SEM technology and also a specialized instrument industry for this application exists. Nevertheless, critical details about equipment developed outside the academic community are very often confidential. Another family of dedicated instruments consists of laboratory equipment composed for basic research tasks and although their development often began with a commercial microscope, the volume of modifications was much larger than that described in the previous section. One example is the UHV SEM working within the range 100 eV to 3 keV with resolution of 60 nm at 250 eV and equipped with a LEED pattern detector consisting of two concentric hemispherical grids, two microchannel plates, and a two-dimensional detector. The specimen was typically inclined 45 ~ toward the detector that was, moreover, rotatable around the sample. Signal processing functions included selection of a diffraction spot for the brightfield imaging and for various dark-field images. This device, based on a Hitachi S-800 but completed by equipment typical for surface analysis devices including the magnetically driven transfer from the air-lock, provided many interesting observations, e.g., of grains on polycrystalline Si, the step structure on a Si (111) surface, domain structure on the reconstructed Si (110) 16 x 2 surface (Ichinokawa et al., 1987), and also of superstructures and of movement of islands on an Au-evaporated Si (111) surface (Ichinokawa et al., 1986). In order to collect and process the image
404
MOLLEROVA AND FRANK
FIGURE47. UHV SLEEM for examination of clean and defined surfaces (the magnetically driven specimen transport is not attached to the air-lock on the far right-hand end). data, the authors of these studies made enormous effort with their electronic equipment, the quality of which was far below that of the present. In the authors' laboratory an UHV SLEEM instrument has been developed, the design representing a combination of the "adapted SEM" outlined above (i.e., biased specimen and detector according to Figure 37) and facilities usual in surface analysis equipment for examination of clean and defined surfaces (clean UHV conditions of the order of 10 -8 Pa, separate preparation chamber with the ion gun for cleaning and sputtering the surface, and with an attachment for evaporation of m e t a l s ) see Figure 47. The basic illumination system is the commercial electrostatic two-lens column with a Schottky cathode (2LE Column, FEI Company; see http://www.feibeamtech.com/pages/electron.html). The apparatus is intended to employ diffraction, interference, and energy-band contrasts and will be equipped with a two-dimensional LEED pattern detector the design of which has not been finished yet and with a parallel operating electron
SCANNING LEEM
405
FIGURE 48. Double-tilt specimen stage for the device in Figure 47, permitting insertion of a specimen cartridge via the air-lock with five high-voltage connections to outside of the vacuum chamber.
energy analyzer of the hyperbolic type (Jacka et al., 1999) that is under preparation. As we saw in Section VI.E, even a tiny specimen tilt manifests itself with large beam impact angles at the lowest energies. In order to acquire full control over the impact direction, a double-tilt specimen stage is necessary as shown in Figure 48. It features the x and y movements of + 5 mm, z-axis movement of 4- 10.5 mm, rotation of -t-8 ~ and two mutually perpendicular tilts of up to + 5~ One prospective task is to solve a combination of the SLEEM method with surface microanalysis like Auger spectromicroscopy. For this purpose a miniature all-electrostatic SLEEM column has been developed with the built-in detection part shown in Figure 34(b) (see Frank et al., 2000a). The whole device (see Figure 49) is of length 90 mm and diameter 45 mm, and at 5 keV primary energy, probe current of a few nA, and working distance 5 mm, it provides a resolution of 30 nm (E1-Gomati et al., 2002) that predicts a value around 100 nm at 10 eV. The column fits inside a cylindrical mirror analyzer for Auger electron spectroscopy but in a separate installation it can be completely biased to a high positive potential providing for the CL configuration with earthed specimen. Bearing all the previous considerations in mind, we can now outline a design for the ideal dedicated SLEEM instrument for general
406
MULLEROVA AND FRANK
FIGURE 49. Electrostatic three-lens mini-column, equipped with Schottky cathode, two-stage quadrupole centering system, octupole stigmator/centering and built-in detector (see Figure 34(b)) with a six-segment collector. (Reprinted with permission from Frank et al., 2000a.)
very-low-energy SEM applications. Such a device would be similar to the setup shown in Figure 46, i.e., equipped with the positively biased booster and the CL with the specimen at ground potential. For acquisition of diffraction and energy-band contrasts, a two-dimensional multichannel detector is desirable onto which the full LEED pattern would be projected. In order to focus the diffraction pattern, we have to let the signal beam pass through some lens. This can be an IOL and then deflection toward some kind of upper detector is necessary but here the deflection assembly has to image its input plane onto the detector plane, so that behind a weak Wien filter the simple extraction field has to be replaced by regular large-angle deflection unit. Altogether the device becomes relatively complicated so that
S C A N N I N G LEEM
407
a configuration with the single-polepiece lens inserted below the specimen (e.g., a miniature one with permanent magnets) seems to be more promising. Then, the LEED pattern will be formed in the space between the specimen and the SEM column (Mfillerovfi and Lenc, 1992b). Having ample free space available (see Figure 36), we can design the two-dimensional detector on various principles. Of course, the specular beam would still escape detection, but this could be avoided by allowing for a small specimen tilt. Naturally, a field-emission gun of a high brightness is desirable and when designing the specimen chamber as a UHV one, we extend significantly the scope of possible applications.
C. Alignment and Operation If a conventional SEM is adapted via insertion of the CL, the routine procedures for alignment and operation become modified. Let us now make a few remarks on this topic. A key issue is the strong electric field in the specimen chamber. The maximum applicable strength of the field between the specimen and anode within the CL naturally depends on the quality of both surfaces. It is generally recommended to arrange the specimen holder or cartridge so that no sharp edges or protrusions appear on the side facing the anode and to cover the specimen with a large flat cap made of a smooth foil, leaving the desired part of the specimen exposed for observation. It is good practice to start the experiments with every new specimen by "training" the specimen biasing by slow stepwise increase of the voltage with the rest of the microscope switched off. Good optical properties are obtained for sufficiently high values of the immersion ratio k so that the primary energy should not be chosen below 5 keV while 10 keV seems to be an optimum value. Thus, the field strength is mainly controlled via the working distance and according to experience the range between 1 and 2.5 kV mm -1 (i.e., l between 4 and 10 mm) usually suits the purpose. Naturally, when predicting the imaging parameters dependent on the working distance, we have to take into account the necessary underfocusing of the SEM column, connected with the CL optical power (see the next section). We now restrict ourselves to the configuration shown in Figure 37 that has proved to be optimum for adaptation of general purpose SEMs. Two points are important here, namely aligning the detector onto the optical axis and tuning the homogeneity of the CL retarding field. The detector alignment is a standard initial routine used not only when the detector is designed to be retractable as was recommended above but always before entering the SLEEM mode. This routine should be performed
408
MULLEROV,~ AND FRANK
FIGURE 50. An example of the appearance of the microscope screen when the detector/ anode assembly shown in Figure 37 is being adjusted onto the optic axis: (a) the upper surface of the YAG crystal with no specimen bias and only low BSE signal from a specimen composed of light elements; (b) the YAG surface combined with the specimen image in the bore, both images being defocused with the sharp image plane situated between them (specimen biased for an impact energy of 1 keV so that the SE signal dominates).
with a perfectly aligned column, particularly as regards the beam centering. The upper surface of the YAG crystal is treated in the same way as the lower detecting surface so that at low magnifications the scintillator material around the central bore is struck by primary electrons from above and the YAG surface is visible on the microscope screen as a bright area with black circular feature, which can then be easily mechanically adjusted to the screen center (see Figure 50). When afterwards increasing the magnification, we restrict the scanning range to within the detector bore and only the lower YAG surface remains active for electrons emitted from the specimen. This low limit of magnification is usually between 250 and 500, which is one of the drawbacks of this detector type. Nevertheless, modern computercontrolled microscopes enable one to control every active element within the column easily so if a larger field of view is needed, the pivot point of the deflection system can be shifted nearer to the scintillator. This change increases the OL aberrations because of an out-of-axis passage of the beam but the corresponding drop in resolution should not be perceptible owing to the enlarged pixel size. A further step in the recommended procedure is to check whether the position of the detector bore does not move on the screen when refocusing from the detector plane to the specimen plane visible inside the bore; otherwise the OL centering has to be improved. Next the specimen bias is increased in steps and image astigmatism is corrected together with the shift
SCANNING LEEM
409
FIOURE 51. An example of the very-low-energy image in the center of the field of view with the rim of the mirror image connected with glancing electron impact and with their reflection in front of the surface; electron energies from the left: 2.5, 1, 0, and -2.5 eV.
of field of view, which is eliminated via slight specimen tilt. When continuing this until the specimen bias is equal to the gun voltage, we approach the zero energy of electron impact so that from the margin of the field of view the surface image starts to convert to the mirror image of an above-specimen equipotential surface. Now the most sensitive alignment of the CL field can be made by shifting the residual central area of the very-low-energy image into the screen center by using small specimen tilts. If the double-tilt facility is not available, the single tilt can be combined with the specimen rotation. Sometimes small corrections of the OL centering are made but this is a pragmatic step not belonging to the consistent alignment procedure. This step of the alignment procedure is illustrated in Figure 51. Roughly below 5 eV some signal decrease in the center of the field of view starts to appear owing to loss in signal escaping through the detector bore, as follows from Figure 38. At low magnification, the margin of the field of view appears (see the next section, Equation (60)) and shrinks with further reduction of the energy. Around the field of view, a rim of mirror image is seen where electrons reflect on above-surface equipotentials. When the zero energy is reached, the specimen surface acts as a planar mirror reflecting the lower scintillator surface with the central sink and bore and this image can be focused. The signal deficit in the center of the field of view, analogous to the escape of the (00) diffracted beam, is inherent in coaxial detectors in general. In practice this is avoided by a slight specimen tilt causing only a small loss in resolution. Systematic solution requires using a deflection unit and sidepositioned detector. In a well-aligned device, the very-low-energy image centered according to Figure 51 is seen and the field of view does not move when decreasing the specimen bias throughout its full range. In Figure 51, some residual ellipticity of the central spot is still visible, which indicates that the configuration is not perfectly axially symmetric.
410
MULLEROVA AND FRANK
In the course of the SLEEM mode operation it is always wise not to increase the specimen bias too fast and to use specimen movements, z-shift, tilt, and rotation in particular, very carefully with larger changes better made at a low bias. Interpretation of contrast observed below a few hundreds of eV is often not straightforward and is significantly facilitated when a series of micrographs of the field of view is available within the full energy scale. D. Practical Issues
The optical power of the cathode lens influences the beam impact on the specimen and modifies characteristics like the image magnification, the working distance (when assessed according to excitation of the magnetic focusing lens), and the impact angle connected with beam rocking around the pivot point of the scanning system. Also an additional condition restricting the field of view appears, namely that connected with the increase of the impact angle to rt/2 as is shown in Figure 51. While the restriction to the field of view and increase in the impact angle can be only recognized and considered when interpreting the image, corrections for focus and magnification should be incorporated into the microscope control software. This section aims at preparing algorithms for these corrections (see Zoba6ov~t et al., 2003). The basic equations were given by Mfillerov~ and Frank (1993) while Huta~ et al. (2000) solved the correction of magnification. Let the primary beam trajectory (see Figure 52) be initially directed into a point with radial coordinate r0 that in paraxial approximation is given as r o - ( w s + l ) f l , where Ws is the axial coordinate of the virtual vertex of the scanning system. The field in the anode bore acts as a diverging lens of a focal length fA that moves the virtual vertex to Z----Wst=fAWs(WS--fA)-1. The lens also enlarges f l ~ f l ' and in the paraxial approximation (i.e., when we can put tan fl = sin/3 ~ fl), we get
~ ' - ~ Ws/W~. The homogeneous retarding field further deflects the oblique impacting ray along a parabolic trajectory so that it is easy to trace its radial coordinate and velocity; an interesting point is where the axial velocity falls to zero. This takes place on a fictitious "reflection surface" that intersects the specimen surface at a radial coordinate rmax defining the maximum size of the field of view to Vmax - 2rmax ~
4l 4l + 3ws ~ . 4l + WS
(60)
SCANNING LEEM
411
FIGURE52. The primary beam trajectory inside the objective and cathode lenses. In order to derive Equation (60), the focal length of the aperture lens (Lenc and MiJllerovfi, 1992a) k f A -- --41 k---f-~
(61)
was, for near-zero landing energies, i.e., k > 104, approximated by -41. Assuming W s = 25 mm (see below), l = 5 mm, and E e = 10 keV, we get Vmax = 0.42 mm at the landing energy of 1 eV and 130 gm at a mere 0.1 eV, i.e., quite acceptable figures. It is obvious from Figure 52 that the beam impact angle, which is initially equal to/3 and, owing to the aperture lens action, enlarges to/3', increases further within the retarding field. Solving again the parabolic motion up to the specimen surface, we get for the final impact angle, [3cL, the relation tan/3cL =
sin/3' v/ 1 - k sin 2fl'
,
(62)
412
M(JLLEROV,h. AND FRANK
i.e., this enlargement is roughly k ~/2 times. When substituting for/3' and then from Equation (61), we find near the optic axis
~ CL -
r ~~/--~ WS + I
1 -}
~
W S
k
-~. .
(63)
For a tilted specimen, this impact angle, increasing linearly with the off-axis distance, combines with the uniform impact inclination shown in Figure 44. The above-described changes in the parameters of the field of view are inherent in the configuration and although we can modify them to some extent by controlling the vertex position ws, actual correction for them is neither possible nor desired. On the contrary, changes in magnification and in the efficient working distance should be automatically corrected in the control software. In the paraxial approximation the coordinate rc of the impact point (see Figure 52) amounts to r c = ( 2 1 e + Ws')fl' with e = k l / 2 / ( 1 + kl/2). Let us define the magnification correction factor A M = ro/rc < 1, which can be used for updating the size of micron marks or the numerical magnification values. From previous relations we can write this as AM =
fA(Ws + l)(~/-k + 1) . fA WS(~/-~ + 1) + 2lVCk(fA - ws)
(64)
It should be noted that A M does not represent the CL magnification, which is, of course, not Ws dependent. When substituting forfA from Equation (61), we get at k >> 1 the factor A M e (1/2, 2/3) within full range of ws/l; the most often met value is A M ~ 0 . 6 . Careful measurement of A M showed that the approximation (61), derived while considering an abrupt change of the CL field in the anode plane, does not provide values o f fA fitting the measured data with accuracy sufficient for the purposes of critical dimension measurement for example. Hence a more exact relation was derived, based upon modeling the anode field of a finite thickness t within which both the axial potential and the electron trajectory follow parabolic curves. Lenc and Mtillerov~i (1992b) used this approach when deriving relations (42) and (43) for the CL aberrations. The result was k X 4 - ln(1 - X2) - 1 , )CA---41 k- 1 2 Arth X
E
I
X --
k
It 1"
(65)
SCANNING LEEM
413
Finally we will look at the magnitude of underfocusing Af that has to be made with the magnetic OL when the cathode lens is excited. In a similar way as above, we find in the paraxial approximation that the surface point is imaged by the retarding field at a distance 21e below the anode. The aperture lens in the anode plane further images this virtual crossover so that it appears near a point lying at a distance of 1/3 below the specimen; more accurately, the axial shift of the focused probe is given by
A f -- --l 21x/k + fA ( ~ -- 1) > 0. 21x/-k -- f A (~/-k + 1)
(66)
In order to obtain a rough quantitative estimation, we use fA from Equation (61) and k >> 1 and get A f ~ ( l / 3 ) [ 1 - ( 8 / 3 ~ ) ] . This leads to a slope of the refocusing, necessary when the energy varies, expressed as 3(Af) ~ -
OE
-
41 9~/EpE
o
(67)
For example, with l = 5 mm and E p = 10 keV we get 7 gm eV -1 at 10 eV. Equations (64) and (66), each in combination with Equation (65), represent the desired algorithms for the on-line correction of magnification and for the refocusing. Both algorithms contain three parameters, Ep, l, and t, while A M depends also on the vertex position Ws. Values of t and Ws cannot be directly measured and in fact they represent some effective dimensions obtainable only by fitting experimental data to the model. This was made in one particular SLEEM arrangement and the result was Ws= 25.62 mm (with the OL aperture situated at 27 mm above the anode) and t-- 5.79 mm for an anode bore of D = 3.5 mm. The ratio t/D = 1.65 for an anode thickness of 2 mm corresponds accordingly to a ratio of 1.25 for a thin anode (Lenc and Mfillerovfi, 1992b). Furthermore, for a broad range of variables the measured magnification factors AM(l, E) fitted the above model with deviations below 1.9% including the measurement errors (Huta[ et al., 2000).
VIII. SELECTED APPLICATIONS
This section summarizes the results of some demonstration experiments in which the aim was to map the main features of SLEEM micrographs at low and very low energies for a particular family of specimen types and
414
MOLLEROVAAND FRANK
to verify the feasibility of obtaining the types of contrast inherent in slow electrons. Only in Sections VIII.D and VIII.I do we quote results of more systematic studies.
A. Prospective Application Areas First of all let us briefly characterize the application areas in which the use of the SLEEM mode can contribute to progress in the solution of research tasks. It is well established that examination of semiconductor structures, both as regards their geometry and critical dimensions and the local voltages and currents, either initiated by powering the structure or induced by the electron beam, is best performed at beam energies around 1 keV. Dedicated IC testers use this energy and many of them are equipped with some retarding field element. The doping contrast is highest around 1 keV, too, and a further possibility is to use the elastically backscattered electrons at a tailored very-low-energy causing no damage. Nonconductors were for a long time observed below their critical energy where only a moderate charging takes place. This mode was, of course, surpassed by observation just at the critical energy, as described in Section VIII.D. However, a new approach has arisen consisting in controlled return of the fraction of SE needed to balance the charge so that the noncharging situation can be secured at any energy but still only below Ec2. Detailed examination of surface topography is best made at an electron energy for which the interaction volume inside the specimen fits in size the relief protrusions. To a certain extent this remains valid even at energies for which the primary electrons do not penetrate to below the escape depth of SEmif a raised feature is just filled with the interaction volume, even SE directed quite far from the surface normal might be emitted. For details smaller than 100 nm this means that the low-energy range must be used. These small features replace the topographical contrast of inclined facets and surface steps, dominating at high energies. Variations in the electron yield with crystal orientation culminate at a few hundreds of eV, which energy range is then optimum for observing grains in polycrystals, crystallinic precipitates, and amorphized areas in crystals. The diffraction and interference contrast below, say, 20 or 30 eV reveals phenomena connected with surface crystallinity and its changes owing to surface reconstructions, adsorption, desorption, growth of layers, sublimation, diffusion, segregation, etc.
SCANNING LEEM
415
This list obviously covers selected but very numerous tasks from virtually any of the application fields of microstructure examination, both in materials science and the life sciences.
B. General Characteristics of Micrograph Series Because of the lack of experience with contrast appearing in micrographs below, say, 500 eV, it is good practice to acquire always (or at least with a new type of specimen) a series of micrographs beginning with the primary beam energy used and continuing by increased specimen bias, possibly up to near the zero energy. When doing this, attention should be paid to preserving the identical field of view and to correcting for the magnification changes wherever this is not performed automatically. This micrograph series will show some characteristic features that include disappearance of the edge effect, transformations in the material contrast, and enhancement of the relief contrast. Further image changes with decreasing electron energy are then inherent to individual structure types. One example is seen in Figure 53, which shows the surface of a Cu polycrystal with the surface oxides and contaminants removed by chemical etching. While at 5 keV the image is strongly dominated by the edge effect appearing on steps made by etching along grain boundaries and also on other etch pits, at 200 eV these over-brightened features are not visible. Instead, the fine surface relief combined with the grain contrast appears as most pronounced. At 10 eV the contrast of residual islands of
FIGURE53. Surface of a polycrystalline Cu sheet etched in nitric acid, Tesla BS 340 SEM adapted for the SLEEM method, energies from the left 5 keV, 200 eV, and l0 eV, the width of the field of view is 70 gm. (Reprinted with permission from Miillerovfi and Frank, 1994).
416
MOLLEROVA AND FRANK
FIGURE 54. GaAs-based integrated circuit, JEOL JSM T220A SEM adapted for the SLEEM method, electron energies (a) 9800 eV, (b) 4300 eV, (c) 1400eV, (d) 20 eV; the width of the field of view is 400 gm. contamination is strongest; the mechanism would require further examination in order to be explained, a surface microanalysis in particular. Another typical example, shown in Figure 54, represents the semiconductor structures. Here one can notice primarily the contrast changes caused by decreasing penetration depth as interfaces between technological layers are crossed, which projects itself into variations in the BSE and SE2 yields. Possible dynamic effects, connected with injection of electrons into interface states and creation of space charges within the information depth, would also need further examination. At 20 eV the local charging and surface details and defects are most obvious. This micrograph series also illustrates the noncorrected changes in the image magnification with decreasing electron energy. The third example in Figure 55 consists of only a single micrograph representing a typical example of an unexpected contrast that appeared at low energies without being apparent at all at 10 keV. The dots arranged in rows on a cleaved GaAs crystal surface might represent islands of oxide layer preferentially grown on crystal defects or on edges of surface steps made when cleaving but no reliable explanation is at hand. Again, surface microanalysis would greatly facilitate the interpretation.
SCANNING LEEM
417
FIGURE 55. "Decoration dots" on the fracture surface of a low-quality GaAs crystal, Tesla BS 343 SEM adapted for the SLEEM method, electron energy 250 eV, the width of the field of view is 20 gm.
C. Surface Relief In all the series of micrographs in this section, strong enhancement of the relief contrast is apparent when they are made within a broader energy range. At flat metal surfaces without any artificial structure, small relief details are best visible around 50 eV where the penetration depth is shortest. In Figure 56 two frames from the first published series of micrographs, taken throughout the full energy scale, demonstrate this trend. We notice here that although the detector system shown in Figure 37 that was used to acquire the majority of the micrographs is of the overhead type and should not produce any shadowing effects, in practice this is not entirely true. The scintillator is placed in an axially symmetrical position but the side-attached light guide breaks the symmetry and the efficiency of light transport is not identical all over the scintillator crystal even if the optical contact is made properly. Owing to the strong acceleration within the CL field, the emitted electrons more or less preserve their off-axis coordinates and species emitted from any one pixel impact the detector locally. Consequently, the image side situated below the light guide is the brightest (see Figures 50 and 51) and sometimes some off-line corrections are needed at very low energies. In connection with this, larger surface facets inclined toward the light-guide direction might also exhibit a higher signal and hence some kind of moderate shadowing is observed.
418
MOLLEROV~i.AND FRANK
FIGURE56. Chemicallyetched polycrystallineTi sheet, Tesla BS 350 UHV SEM adapted for the SLEEM method, electron energies 15 keV (left) and 50 eV (right), the width of the field of view is 50 ~tm.(Reprinted with permission from Mfillerovfiand Frank, 1993).
D. Critical Energy Mode In Section III.E, we discussed phenomena connected with charge accumulation in nonconductive specimens and saw that if the total electron yield curve cr(E) is taken as the process diagram, then spontaneous movement of the working point toward the critical energy Ec2 does qualitatively explain the observed effects. In addition, it was argued that when the electron energy is below Ec2 , the ultimate (positive) surface potential is reduced because of recapture of the slower part of the SE. It is important to recall that, irrespective of the initial energy of impact, the charging process causes shifts of the impact energy, influenced by fields of persisting charges, directed always toward Ec2. This is, of course, connected with corresponding changes in the image signal; Figure 57 illustrates this for the alternative of a positive charging up. This is a well known effect encountered in the observation of nonconductors and can be utilized via a practical procedure consisting of a temporary increase of the image magnification and subsequent relative assessment of the signal level from the smaller field of view with respect to its surrounding, which reveals in what direction the charging has changed the average emission (see Joy and Joy, 1996). The same approach forms the basis for an automatic method of determination of Ec2 (or, more exactly, of the energy causing minimum damage of the image owing to charging), which is also outlined in Figure 57. The method (see Frank et al., 2001) consists in acquisition of a temporal sequence of image signals from individual pixels since their first illumination, and in off-line determination of the integral under the S(t) curve, which can be taken as a measure of the total signal change caused by the charge accumulation. By plotting this quantity versus the initial impact
SCANNING LEEM
.
.
.
.
,
.
419
.
I IMPACT m I ENERGY ! !
Ec,
E8
Ec~
E
t2 S
Q
,%o t
Ec~
E8
FIGURE 57. Scheme of the spontaneous time development of the image signal in the course of positive charging up: movement of the "working point" from initial (Es) to final (EF) impact energy (top), signal vs. time plot (bottom left), and the area below the S(t) curve (the charging rate) as a function of the initial impact energy (bottom right). (Reprinted with permission from Zoba6ovfi and Frank, 2003.)
energy, we can find its optimum value where the curve crosses the zero level. The peculiar behavior of this curve below Ec2 was explained as a consequence of SE being "focused" into the detector bore by the radial field component above the charged field of view surrounded by the noncharged specimen (Zoba6ov~t and Frank, 2003). The results, demonstrated in Figure 58, are more reliable for flat specimens exhibiting only moderate heterogeneity in the conductivity and electron yields. The observation method described in this section requires modifications in the SEM control software that go beyond the scope of a simple adaptation made by the customer. It is mentioned here to demonstrate that, when working just at the critical energy, we can achieve much better results than at low energies in general. The same idea led to the above-described detection approach incorporating controlled return of a portion of the SE.
E. Diffraction Contrast In Section IV.B, we dealt with the electron backscattering from single crystals and hinted at the possibility of obtaining image contrast connected with locally varying fulfillment of the diffraction condition. This consists in getting a bright albeit defocused diffracted beam(s) incident on the detector, which is, for the detector types described here, achieved automatically except for the specular spot (00). Although at very low energies the reciprocal lattice is theoretically two-dimensional and bright spots are
420
MULLEROV,~i AND FRANK
FIGURE 58. Surface of writing paper, nonprocessed and uncoated, Tesla BS 343 SEM adapted for the SLEEM method, electron energies (a) 3650 eV, (b) 2650 eV (the critical energy Ec2), and (c) 1850 eV; the width of the field of view is 40 gm. (Unpublished micrographs courtesy of M. Zadra~il.)
received at any energy, in fact significant variations in the spot brightness with electron energy are always observed. Consequently, the eBSE signal from crystals is modulated along the energy scale according to the crystal orientation and the distance from the Ewald sphere of a nearby reciprocal lattice point. Also, additional features can appear owing to effects going beyond the kinematical diffraction theory. The first test experiment was published and interpreted in detail by Frank et al. (1999). In Figure 59 we see micrographs taken at normal impact of the slow electron beam. One can compare the brightness of rectangular (with (100) orientation) and triangular (with (111) orientation) Pb crystals on Si and verify that it varies with energy in different ways in the two cases; this difference can be correlated with the diffraction condition for individual configurations. The interpretation of Figure 60 in which the micrographs are taken with the specimen tilted by a mere 1.3 ~ is much more sophisticated.
FIGURE 59. Flat Pb islands deposited in situ onto an Si (100) surface, JEOL JAMP 30 UHV SEM adapted for the SLEEM method, electron energies (a) 5, (b) 12.5, (c) 42.5, and (d) 378 eV, the width of the field of view is 60 gm. (Reprinted with permission from Frank et aL, 1999.)
SCANNING LEEM
421
FIGURE 60. The same specimen and microscope as in Figure 59, the specimen tilted to approximately 1.3~ in the direction inclined at 55~ with respect to the horizontal line, electron energies from the top left by rows: 6.5, 7.5, 10.5, 16, 18, 22, 29, and 34.5 eV; the width of the field of view is 50 gm. (Reprinted with permission from Frank et al., 1999.)
Now, not only the crystal orientation and energy but also the impact angles, both polar and azimuthal, play a role as they define the incident ray orientation with respect to the reciprocal lattice. Hence even crystals with an identical crystalline plane on the surface but mutually rotated exhibit some specific behavior of the eBSE signal with energy. In connection with this experiment, the degree of the illumination coherence was also assessed according to relations given in Section IV.C. The size Dc of the coherently illuminated area was determined according to Equations (29), (31), and (32) and also the condition (30) for the source size was verified. The experimental data were taken as A E = 0 . 5 eV, E p = 10 keV, a c = l mrad, E = 1 0 eV, and dhk=3 nm. Considering the OL demagnification to be 10 times, we have or0 = 0.1 mrad for the diaphragm illumination angle in Figure 15, and finally we get ot = 30 mrad for the aperture angle on the specimen. Then the factors limiting Dc result as IAsl = 15.5 nm, we = 12 nm, and wo= 6.4 nm for 0=re/2 with increase to 9.1 nm at 45 ~ The real spotsize was not measured but could be estimated to be between 10 and 20 nm. Obviously, the constructive interference took place at least for a major part of the primary spot, which means that at
422
MOLLEROV,~i AND FRANK
favorable conditions the image signal was increased by a factor approaching the number of unit cells within the coherence area or within the crystal domain, whichever is smaller. It is obvious that observations like these can be made solely on very clean surfaces and under true UHV conditions. However, it should be underlined once more that these demands do not arise from the observation method employing very slow electrons but they condition the phenomena that can be observed. Prospective applications of the diffraction and interference contrast mechanisms can be estimated according to the huge variety of experimental results collected by means of the LEEM apparatus (see, e.g., Telieps and Bauer, 1985; Telieps, 1987; Bauer and Telieps, 1988; Tromp and Reuter, 1993; Tromp et al., 1993; Bauer, 1994; Tromp, 2000). A survey of references in this area can be found at http://www.leem-user.com.
F. Contrast of Crystal Orientation In the previous section the examples showing a crystallinic structure in verylow-energy micrographs concerned the coherent backscattering when the detected yield is increased by amplitude instead of intensity addition of scattered waves. However, in Sections IV.B and IV.D we also mentioned the dependences of both BSE and SE yields on the crystal orientation and argued that these should become more pronounced at low energies. In fact, experiments showed that for metal polycrystals the grain contrast in SLEEM images is highest between 50 and 150 eV (see Figures 53 and 56). Another application of the same effect arises when amorphous and crystalline areas are to be distinguished. The example in Figure 61 presents a lattice of spots amorphized by laser beam exposure of a crystalline layer. Owing to this amorphization, a decrease in both SE and BSE signal can be generally expected so that brighter centers of dots, caused by increased laser beam power, need to be examined in more detail. Figure 61 illustrates the enhanced sensitivity of slow electrons to spurious a.c. electromagnetic fields. The vertical stripes are caused by an excessively high amplitude of the 50 Hz interference from the SEM electronic console.
G. Layered Structures One trivial consequence of lowering the impact energy is that thin surface layers that were transparent at high energies become opaque and their structure can be observed. The example in Figure 62 shows a trilayer structure prepared for exploration of the backscattering factor in Auger
SCANNING LEEM
423
FIGURE 61. Structure created by laser beam exposure of microdots (with various beam intensities and exposure times) in a Pt3Si layer made on a glass substrate, dot pitch 2.9 ~tm; Tesla BS 343 SEM adapted for the SLEEM method, electron energy 200 eV. (Specimen provided by Dr. H. Birecki, HP Labs; reprinted with permission from Mtillerovfi, 1996.)
FIGURE 62. A patterned multilayer structure consisting of islands of a 500 nm thick Au layer (right) on a Si substrate, partially covered with a 200 nm thick layer of GeSi (top left), JEOL JSM T220A SEM adapted for the SLEEM method, electron energies 9800 eV (left) and 850 eV (right), the width of the field of view is 300 gm. (Specimen provided by Professor M.M. E1-Gomati, University of York, UK.) s p e c t r o m i c r o s c o p y ( E 1 - G o m a t i et al., 1992) w i t h a n o b v i o u s d e m o n s t r a t i o n o f this effect. S p e c i m e n s o f s e m i c o n d u c t o r devices in a p l a n view, like t h a t in F i g u r e 54, e x h i b i t t h e s a m e f e a t u r e s b u t c o m b i n e d w i t h o t h e r effects a n d h e n c e are n o t so striking.
424
MfOLLEROVA AND FRANK
FIGURE 63. A beveled cross-section cratered by oblique impact of a low-energy ion beam across a multilayer structure consisting of 12 pairs of 100 nm GaAs/63 nm AlAs layers; Tesla BS 343 SEM adapted for the SLEEM method, electron energies from the top left by rows: 20, 30, 40, 130, 430, and 2430 eV; the width of the field of view is 600 gm. (Specimen provided by Dr. J. Kovfi6, TU Bratislava, Slovakia, preparation by Dr. A. Barna, KFKI Budapest.)
Unlike the previous example, the structure in Figure 63 produces contrasts that are not so easy to understand. The beveled section of a multilayer, composed of two alternating different semiconductors, shows outcrops of layers of one material (GaAs instead of AlAs) at a strongly elevated contrast within a certain energy interval, and in addition three stripes of different intensity instead of two can be distinguished periodically repeating across the structure. One boundary of the "extra" bright strip, namely that next to the dark part corresponding to the thicker wedge, is not sharp, which indicates that the contrast source might be buried. And in addition, the effect, i.e., both the contrast enhancement and formation of the third fuzzy strip, is clearly of a dynamical nature as can be seen from Figure 64 where none of the previous effects appears at the lowest electron dose while both features progressively emerge with increased current as well as with prolonged frame time. Similar effects were observed with Mo/Si multilayers (Mfillerovfi et al., 1997) but they were absent at metallic multilayers such as Ni/Cr. The phenomenon will be further studied because the provisional interpretation, relying upon the influence of charges trapped in the interface states and forming a buried space charge layer, needs to be
SCANNING LEEM
425
FIGURE 64. The same specimen and microscope as in Figure 63; electron energy 450 eV, the width of the field of view is 600 gm, primary beam current 0.2 nA (upper row) and 80 pA (lower row), frame times from the left 3, 11, 30, and 83 s. (Reprinted with permission from Mfillerovfi et al., 1997.)
supported by more experimental data; furthermore a complete model of the contrast mechanism, even qualitative, is not available yet.
H. Material Contrast
The absence of the monotonic material contrast in the BSE emission, i.e., the direct proportionality 17 o( Z, available at conventional beam energies in SEM, is characteristic of the low-energy ranges. This fact is obvious from the t/(E) plots in Figure 13 for clean material surfaces. A comparison of clean and "real" surfaces in Figure 14 indicates that, under standard vacuum conditions and on specimens without any special treatment, some residual traces of this contrast can be observed down to about 1 keV. Below 1 keV any relations between BSE yields from different materials have to be specifically reconsidered. As Figure 29 shows, even the contrast between gold and carbon, otherwise representing the extreme in this respect, is inverted or at least disappears at 20 eV, where the eBSE emission already dominates. When following a particular combination of materials throughout the energy scale, even more than one inversion can be registered; Figure 65 shows two of them for the Cu/Si combination and both are met at energies for which the Cu layer is far from being penetrated so that no alternative explanation is possible.
426
MULLEROV,~ AND FRANK
FIGURE 65. Islands of a 300 nm thick Cu layer deposited through a mask, exposed by electron beam lithography, onto the Si substrate, period of squares is 10 ~tm; Tesla BS 340 SEM adapted for the SLEEM method, electron energies from the top left by rows: 5000, 500, 250, 100, 50, and 10 eV. (Specimen provided by Mgr. F. Mat~jka, ISI Brno, Czech Republic.)
On the other hand, for a particular couple of materials that at high energies exhibit a moderate contrast because of a small difference in atomic numbers only, in the low-energy range an energy value can be tuned for which much enhanced contrast is available (Mtillerovfi, 2001). Figure 65 also illustrates consequences of the bad practice consisting in performing the alignment, stigmation, and focusing inside the field of view selected for the final frame. Rectangles of the graphitic layer of contaminants, which are always formed on specimens but at high energies are usually transparent enough, heavily damage the images at low energies and particularly around 100 eV, albeit the sign of the material contrast remains preserved.
L Electronic Contrast in Semiconductors
Observation of doped areas with respect to the semiconductor substrate, both in plan view and on cleaved cross-sections, is one of the major tasks of microscopists, imposed by the semiconductor industry, which is faced with requests for continued diminution of the size of features and increase of the throughput. Several times we recalled the instrumentation branch of IC testers that are represented by low-energy SEMs with special sophisticated attachments. However, the basic question, how to get the best visualization
SCANNING LEEM
427
of the doped areas and what is the correct contrast interpretation, does not seem to have been definitively answered so far. It is obvious that no material contrast can reveal the dopant concentrations as low as 1016 to 1019 cm -3, when in a matrix of 5 x 1022 cm -3 of silicon atoms. Still, successful observations have been made since the mid-1990s and interpreted via the electronic contrast mechanism. Mtillerovfi et al. (2002) reviewed the previous studies and summarized the present situation in understanding the dopant contrast. The main points are that this contrast is observed in the SE emission, achieves up to 10% level when calculated from the equation
Cp/. -
S~
(68)
with Sp and Sn as the mean signal levels in p- and n-type areas, respectively, that p-type generally appears brighter than n-type, and that Cp/n grows toward low energies. In Figure 66 the main ideas are represented of the contrast model described by Sealy et al. (2000), which relies upon differences in the ionization energy; i.e., a distance between the valence band top and the vacuum energy. Because the tiny content of dopant cannot change this characteristic, the ionization energies Ep and E~ are considered identical but the local "vacuum" level varies in the model, being then balanced via abovesurface patch fields created by surface dipoles of nonconstant density. When the patch fields disappear at a distance comparable with the sizes of the doped areas, some average reference energy level is progressively reached sufficiently far from the specimen. A consequence is that electrons to be emitted from the n-type area have to surmount a barrier higher by some AE~. The flat band situation, shown in Figure 66, is modified when the presence of the surface states is taken into account, namely so that the band bending causes a drop in AE, and hence a contrast decrease. For the Fermi level pinned mid-gap at a high density of surface states, no contrast should be observed. The SLEEM observations were made on a boron-doped p-type patterned structure fabricated in an n-type Si substrate using two instruments with considerably different vacuum conditions (Mfillerovfi et al., 2002). The experiments (see Figure 67) confirmed the basic premises of the model, i.e., no BSE contrast and a moderate contrast in the SE emission. However, the most important finding was that significant increase in contrast was registered in the SLEEM mode. Careful contrast quantification verified the high contrast for the specimen inserted into the CL and revealed that even vacuum conditions play a very important role: at a standard vacuum of the
428
MULLEROVik AND FRANK
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Evac,p ESEM
Eil I .......
Evac,n
Ep
Ec,p En
Ec,n
X
EF
Ev, p Ev,n FIGURE 66. Combined band structures of p and n regions in the same specimen, with no influence of surface states assumed.
FIGURE 67. Boron-doped (1 x 1019 cm-3) p-type patterns on an n-type phosphor-doped (4 to 6 x 1014 cm -3) Si (111) substrate: (a) BSE image at 10 keV, (b) SE image at 10 keV, (c) SLEEM image at E~,= 10 keV, E = 1 keV; Tescan Vega 5130 SEM adapted for the SLEEM method, the width of the field of view is 350 gm for (a) and (b) and 500 gm for (c). (Specimen provided by Ing. B. Ne6asovfi, Tesla Sezam, Inc., Ro~nov p/R, Czech Republic.) o r d e r o f 10 -3 to 10 -4 Pa the c o n t r a s t clearly surpasses t h a t o b t a i n e d u n d e r clean U H V c o n d i t i o n s ( F i g u r e 68). T h e existence o f the e x t r e m e l y high c o n t r a s t for a specimen i m m e r s e d into a m o d e r a t e electric field n o t exceeding 2 V g m -1, i.e., w e a k e r t h a n fields n o r m a l l y applied to s e m i c o n d u c t o r structures u n d e r o p e r a t i o n , a n d the e n h a n c e m e n t u n d e r
S C A N N I N G LEEM
429
Cp/n [%] 20
10
102
103 E[eV] 104
FIGURE 68. The electron energy dependence of the SLEEM image contrast between p and n areas for the specimen shown in Figure 67; (A) dedicated UHV SLEEM microscope (see Section VII.B), (B) standard vacuum conditions, (C) SE signal from a standard ET detector. ((B) and (C) from Tescan Vega 5130 SEM adapted for the SLEEM method.) .
.
.
.
,
30
Cp/n [%] 20
iiii
10
ii
i
2
i
4
i
6
i
8
10
Ep [keY] FIGURE 69. The p/n contrast measured in the SLEEM mode for constant impact energy E = 1 keV but variable primary energy E/,.
routine vacuum conditions are facts very promising for application of the SLEEM method in semiconductor diagnostics and testing. The influence of the CL field is further illustrated by Figure 69 showing directly the contrast dependence on the field strength. The low-field limit obviously fits the contrast level achieved with the standard ET detector (see Figure 68). The crucial role of the vacuum conditions clearly indicates that the realization about the clean crystal surface as a base for the contrast interpretation is not correct. Further experiments showed that the contrast
430
MULLEROV~ i. AND FRANK
could be manipulated and even inverted by coating the structure with metals of various work functions. On this basis a new model was proposed (E1-Gomati et al., 2003) that considers the surface to be covered by a graphitic layer of contaminants with quasimetal properties and a metal-semiconductor junction to be formed beneath the surface. The subsurface fields, connected with the junction, explain successfully the observed phenomena even in cases when no patch field can be created, for example with the metalized surface that has to be taken as an equipotential one.
J. Energy-Band Contrast
In Section III.A.2, we described the reflection of very slow electrons on energy gaps, i.e., a contrast mechanism quite exotic from the point of view of SEM practice. In Figure 5 this was illustrated by measured energy dependences of the (00) spot intensity for two crystal orientations of tungsten. However, demonstration of this contrast in a SEM micrograph is difficult--any bicrystal and/or polycrystal specimens exhibit a combination of contrasts caused by phenomena anisotropic with respect to the crystal orientation so that reliably extracting this contribution is a problematic task. One exception is a semiconductor structure with patterned doping, observed in plan view. A clean semiconductor surface can be believed to possess identical properties on the doped pattern as well as on the substrate and the same holds for the crystal orientation in the sense that a small amount of dopant cannot change the electron yields. Nevertheless, additional impurity levels in the energy-band structure, namely those appearing in the energy gaps, can manifest themselves via this contrast mechanism. If such an energy level is hit, electrons penetrate into the doped pattern but not into the surrounding substrate so that the pattern appears dark. The first successful observation was announced by Mfillerovfi et al. (2001) and is shown in Figure 70. A signal decrease is apparent in micrographs taken at 3 and 1 eV and very pronouncedly in the 0.5 eV frame. This first experience has proved that this type of contrast is strongly dependent on even a tiny mechanical tilt of the specimen incorporated into the cathode lens. Figure 70 was taken with a provisional specimen stage with no tilt facility. Hence no true CL field alignment was possible and influences of inhomogeneity of the retarding field could be only compensated by suitable misalignment of the objective lens, which resulted in lowered resolution and enhanced axially nonsymmetric aberrations.
SCANNING LEEM
431
FIGURE 70. A p-type rectangle on the specimen shown in Figure 67, the SLEEM image at the electron energies from the top left by rows: 7, 4, 3, 2, 1, and 0.5 eV; dedicated UHV SLEEM microscope (see Section VII.B), the width of the field of view is 70 gm.
IX. CONCLUSIONS The element of instrumentation common to the history of work summarized in this text, the cathode lens, is in fact a very simple and very old assembly that can be easily incorporated into any electron optical device. In spite of this, it took more than 10 years before it started to appear frequently in the titles of papers in the journals devoted to scanning electron microscopy and its applications. The authors of this review feel a certain satisfaction about this development and about the forthcoming commercial devices containing this attachment, which may belong to the family of dedicated instruments for IC technologies or even to general purpose SEMs. Progress in this direction can break the "magic ring" and the increasing number of instruments will expand the community of users who quickly extend the application fields, etc. A U H V version of the instrument, equipped with devices for surface microanalysis methods, opens the way to examination of fascinating physical phenomena taking place on crystal surfaces that were revealed by the L E E M method. The scanning counterpart can take advantage
432
M(3LLEROVA AND FRANK
of multiple signal acquisition and simultaneous compilation of separate image slices for individual diffraction spots, possibly even completed by additional signals. More experienced users with some technical background can introduce the method into their commercial SEM instruments by an effort comparable with embarking on any other small nonstandard adaptation. For a boosterequipped SEM the adaptation might be quite trivial. In the near future, the first commercial SEM with the CL mode among the standard operation routines is expected. But, as for any other experimental method, the future progress of this method will also depend on its usefulness for a sufficiently broad community of users.
ACKNOWLEDGMENTS
This chapter reviews a major part of the work of the authors' team since the beginning of the 1990s. In the course of this time several particular projects have been brought to a successful conclusion under support of the Grant Agency of the Czech Republic and of the Grant Agency of the Academy of Sciences of the Czech Republic. The final period was supported by the GA ASCR grant no. A1065901. The results presented were naturally obtained in collaboration with other team members, both present and past, in particular Dr. Martin Zadra~il, Mr. Pavel Klein, and Mr. Mojmir Sirn~. The participation of other members of the Institute of Scientific Instruments of ASCR in Brno and the Institute's background in general were crucial for the whole long-term program. External cooperation was most intensive with Professor E. Bauer (TU Clausthal, Germany, and later the Arizona State University) and with Professor M.M. E1-Gomati (University of York, UK). The authors express their profound gratitude to all who helped them in their work. The final manuscript was compiled during a fruitful stay at the University of Toyama, Japan, for which sincere thanks are due to Professors S. Ikeno and M. Shiojiri and to Dr. K. Matsuda.
REFERENCES Autrata, R. (1989). Backscattered electron imaging using single crystal scintillator detectors. Scanning Microsc. 3, 739-763. Autrata, R., Hermann, R., and Mfiller, M. (1992). An efficient single crystal BSE detector in SEM. Scanning 14, 127-135.
SCANNING LEEM
433
Autrata, R., and Hejna, J. (1991). Detectors for low voltage scanning electron microscopy. Scanning 13, 275-287. Autrata, R., and Schauer, P. (1994). Behaviour of planar and annular YAG single crystal detectors for LVSEM operation, in Proceedings of the Thirteenth International Congress on Electron Microscopy, Vol. 1, edited by B. Jouffrey and C. Colliex. Les Ulis, France: Les 6ditions de Physique, pp. 71-72. Autrata, R., and Schauer, P. (1998). Single crystal scintillation detectors for LVSEM, in Proceedings of the Fourteenth International Congress on Electron Microscopy, Vol. 1, edited by H. A. Calderon Benavides and M. J. Yacaman. Bristol, UK: Institute of Physics, pp. 437-438. Barth, J. E., and Kruit, P. (1996). Addition of different contributions to the charged particle probe size. Optik 101, 101-109. Bartog, I., van Hove, M. A., and Altman, M. S. (1996). Cu (111) electron band structure and channeling by VLEED. Surface Sci. 352-354, 660-664. Bauer, E. (1962). Low energy electron reflection microscopy, in Proceedings of the Fifth International Congress on Electron Microscopy, Vol. I, edited by S. S. Bresse, Jr. New York: Academic Press, pp. D 11-12. Bauer, E. (1994). Low energy electron microscopy. Rep. Progr. Phys. 57, 895-938. Bauer, E., and Telieps, W. (1988). Emission and low-energy reflection electron microscopy, in Surface and Interface Characterization by Electron Optical Methods, edited by A. Howie and U. Valdre, New York: Plenum Press, pp. 195-233. Bauer, H. D. (1979). Messungen zur Energieverteilung von Rtickstreu-elektronen an polykristallinen Festk6rpern. Exp. Techn. Phys. 27, 331-344. Bauer, H. E., and Seiler, H. (1984). Determination of the non-charging electron beam energies of electrically floating metal samples, in Scanning Electron Microscopy, Vol. III, edited by O. Johari. Chicago: SEM, pp. 1081-1088. Beck, S., Plies, E., and Schiebel, B. (1995). Low-voltage probe forming columns for electrons. Nucl. Instrum. Methods Phys. Res. A 363, 31-42. Berry, V. K. (1988). Characterization of polymer blends by low voltage scanning electron microscopy. Scanning 10, 19-27. Bindi, R., Lanteri, H., and Rostaing, P. (1980). A new approach and resolution method of the Boltzman equation applied to secondary electron emission by reflection from polycrystalline aluminum. J. Phys. D." Appl. Phys. 13, 267-280. Bleloch, A. L., Howie, A., and Milne, R. H. (1989). High resolution secondary electron imaging and spectroscopy. Ultramicroscopy 31, 99-110. Bode, M., and Reimer, L. (1985). Detector strategy for a single-polepiece lens. Scanning 7, 125-133. B6ngeler, R., Golla, U., K/issens, M., Reimer, L., Schindler, B., Senkel, R., and Spranck, M. (1993). Electron-specimen interactions in low-voltage scanning electron microscopy. Scanning 15, 1-18. Born, M., and Wolf, E. (1975). Principles of Optics. Oxford: Pergamon Press. Brown, A. C., and Swift, J. A. (1974). Low voltage scanning electron microscopy of keratin fibre surfaces, in Scanning Electron Microscopy, edited by O. Johari. Chicago: SEM, pp. 68-74. Bruining, H. (1954). Physics and Application of Secondary Electron Emission. Oxford: Pergamon Press. Brunner, M., and Schmid, R. (1987). Characteristics of an electric/magnetic quadrupole detector for low voltage scanning electron microscopy. Scanning Microsc. 1, 1501-1506. Burns, J. (1960). Angular distribution of secondary electrons from (100) faces of Cu and Ni. Phys. Rev. 119, 102-114.
434
MOLLEROVA AND FRANK
Buseck, P., Cowley, J., and Eyring, L. (1988). High-Resolution Transmission Electron Microscopy and Associated Techniques. London: Oxford University Press. Cailler, M., Ganachaud, J. P., and Bourdin, J. P. (1981). The mean free path of an electron in copper between two inelastic collisions. Thin Solid Films 75, 181-189. Cazaux, J. (1986). Some considerations on the electric field induced in insulators by electron bombardment. J. Appl. Phys. 59, 1418-1430. Cazaux, J. (1996a). Electron probe microanalysis in insulating materials: quantification problems and some possible solutions. X-ray Spectrom. 25, 265-280. Cazaux, J. (1996b). The electric image effects at dielectric surfaces. IEEE Trans. Diel. Electr. Insul. 3, 75-79. Cazaux, J. (1999). Some considerations on the secondary electron emission, 3, from eirradiated insulators. J. Appl. Phys. 85, 1137-1147. Cazaux, J., and Le Gressus, C. (1991). Phenomena relating to charge in insulators: macroscopic effects and microscopic causes. Scanning Microsc. 5, 17-27. Cazaux, J., and Lehuede, P. (1992). Some physical descriptions of the charging effects of insulators under incident particle bombardment. J. El. Spectrosc. Rel. Phenom. 59, 49-71. Cazaux, J., Kim, K. H., Jbara, O., and Salace, G. (1991). Charging effects of MgO under electron bombardment and nonohmic behaviour of the induced specimen current. J. Appl. Phys. 70, 960-965. Chung, M. S., and Everhart, T. E. (1974). Simple calculation of energy distribution of lowenergy secondary electrons emitted from metals under electron bombardment. J. Appl. Phys. 45, 707-709. Czyzewski, Z., and Joy, D. C. (1989). Fast Monte Carlo method for simulating electron scattering in solids. J. Microscopy 156, 285-291. Czyzewski, Z., MacCallum, D. O., Romig, A., and Joy, D. C. (1990). Calculations of Mott scattering cross-section. J. Appl. Phys. 68, 3066-3072. Dahl, D. A. (1995). SIMION 3D Version 6.0, in Proceedings of the Forty-Third ASMS Conference on Mass Spectrometry and Allied Topic. Santa Fe, NM: American Society for Mass Spectrometry, p. 717. Dekker, A. J. (1958). Secondary electron emission. Solid State Phys. 6, 251-315. Delong, A., and Draho~, V. (1971). Low-energy electron diffraction in an emission electron microscope. Nature Phys. Sci. 230, 196-197. Dietrich, W., and Seiler, H. (1960). Energieverteilung von Elektronen, die durch Ionen und Elektronen in Durchstrahlung an dfinnen Folien ausgel6st werden. Z. Angew. Physik 157, 576-585. Ding, Z.-J. (1990). Fundamental studies on the interactions of kV electrons with solids for application to electron spectroscopies. Ph.D. Thesis, Osaka University, Japan. Ding, Z.-J., and Shimizu, R. (1996). A Monte Carlo modeling of electron interaction with solids including cascade secondary electron production. Scanning 18, 92-113. Drescher, H., Reimer, L., and Seidel, H. (1970). Rfickstreukoeffizient und Sekund~irelektronenAusbeute von 10-100 keV Elektronen und Beziehungen zur Raster-Elektronenmikroskopie. Z. Angew. Physik 29, 331-336. Drucker, J., Scheinfein, M. R., Liu, J., and Weiss, J. K. (1993). Electron coincidence spectroscopy studies of secondary and Auger-electron generation mechanisms. J. Appl. Phys. 74, 7329-7339. Egerton, R. F. (1986). Electron Energy-Loss Spectroscopy in the Electron Microscope. New York: Plenum Press. E1-Gomati, M. M., Barkshire, I., Greenwood, J., Kenny, P., Roberts, R., and Prutton, M. (1992). Compositional imaging in scanning Auger microscopy, in: Microscopy." The Key Research Tool, edited by C. Lyman. Chicago: Electron Microscopy Society of America, pp. 29-38.
SCANNING LEEM
435
EI-Gomati, M. M., Romanovsk~,, V., Frank, L., and Mtillerovfi, I. (2002). A very low energy electron column for surface studies, in Proceedings of the Fifteenth International Congress on Electron Microscopy, Vol. 3, edited by R. Cross, J. Engelbrecht, T. Sewell, M. Witcomb, and P. Richards. Onderstepoort: Microscopy Society of Southern Africa, pp. 323-324. E1-Gomati, M. M., Wells, T. C. R., Mtillerovfi, I., Frank, L., and Jayakody, H. (2003). Why is it that diferently doped regions in semiconductors are visible in low voltage SEM? IEEE Trans. Electron Devices, submitted. Everhart, T. E., and Chung, M. S. (1972). Idealized spatial emission distribution of secondary electrons. J. Appl. Phys. 43, 3708-3711. Everhart, T. E., and Thornley, R. F. M. (1960). Wideband detector for micro-micro-ampere low electron currents. J. Sci. Instrum. 37, 246-248. Everhart, T. E., Saeki, N., Shimizu, R., and Koshikawa, T. (1976). Measurement of structure in the energy distribution of slow secondary electrons from aluminum. J. Appl. Phys. 47, 2941-2945. Ezumi, M., Otaka, T., Mori, H., Todokoro, H., and Ose, Y. (1996). Development of critical dimension measurement scanning electron microscope for ULSI (S-8000 series). Hitachi Instrument News Electron Microscopy Edition 30, 15-21. Feldman, L. C., and Mayer, J. W. (1986). Fundamentals of Surface and Thin Film Analysis. New York: Elsevier. Fitting, H.-J., Schreiber, E., Kuhr, J.-Ch., and von Czarnowski, A. (2001). Attenuation and escape depths of low-energy electron emission. J. El. Spectrosc. Rel. Phenom. 119, 35-47. Fourie, J. T. (1976). Contamination phenomena in cryopumped TEM and ultrahigh vacuum field-emission STEM systems, in Scanning Electron Microscopy, Vol. I, edited by O. Johari. Chicago: SEM, pp. 53-60. Fourie, J. T. (1979). A theory of surface-originating contamination and a method for its elimination, in Scanning Electron Microscopy, Vol. II, edited by O. Johari. Chicago: SEM, pp. 87-102. Fourie, J. T. (1981). Electric effects in contamination and electron beam etching, in Scanning Electron Microscopy, Vol. I., edited by O. Johari. Chicago: SEM, pp. 127-134. Frank, L. (1992a). Towards electron beam tomography, in Proceedings of the Tenth European Congress on Electron Microscopy, Vol. 1, edited by A. Rios, J.M. Arias, L. Megias-Megias, and A. Lopez-Galindo. Granada: Univ. de Granada, pp. 141-142. Frank, L. (1992b). Experimental study of electron backscattering at interfaces. Surface Sci. 269/270, 763-771. Frank, L. (1996a). Real image resolution of SEM and low-energy SEM and its optimization. Ultramicroscopy 62, 261-269. Frank, L. (1996b). Width of the SEM and LESEM response function as a tool for the image resolution assessment, in Proceedings of the Ninth Conference on Electron Microscopy of Solids, edited by A. Czyrska-Filemonowicz. Krak6w: State Committee for Scientific Research, pp. 109-112. Frank, L. (2002). Advances in scanning electron microscopy, in Advances in Imaging and Electron Physics, Vol. 123, edited by P. W. Hawkes. San Diego: Academic Press, pp. 327-373. Frank, L., and Mtillerovfi, I. (1994). Zero-charging electron microscopy in a cathode lens equipped SEM, in Proceedings of the Thirteenth International Congress on Electron Microscopy, Vol. 1, edited by B. Jouffrey and C. Colliex. Les Ulis, France: Les 6ditions de Physique, pp. 139-140. Frank, L., and Mtillerovfi, I. (1999). Strategies for low- and very-low-energy SEM. J. El. Microsc. 48, 205-219. Frank, L., Mtillerovfi, I., and E1-Gomati, M. M. (2000a). A novel in-lens detector for electrostatic scanning LEEM column. Ultramicroscopy 81, 99-110.
436
MOLLEROV~i AND FRANK
Frank, L., Mfillerovfi, I., and E1-Gomati, M. M. (2002). SEM visualization of doping in semiconductors, in Proceedings of the Fifteenth International Congress on Electron Microscopy, Vol. 1, edited by R. Cross, J. Engelbrecht, M. Witcomb, and P. Richards. Onderstepoort: Microscopy Society of Southern Africa, pp. 39-40. Frank, L., Mfillerovfi, I., Faulian, K., and Bauer, E. (1999). The scanning low-energy electron microscope: first attainment of diffraction contrast in the scanning electron microscope. Scanning 21, 1-13. Frank, L., Stekb,, R., Zadra~il, M., E1-Gomati, M. M., and Mfillerovfi, I. (2000b). Electron backscattering from real and in situ treated surfaces. Mikrochim. Acta 132, 179-188. Frank, L., Zadra~il, M., and Mtillerovfi, I. (2001). Scanning electron microscopy of nonconductive specimens at critical energies in a cathode lens system. Scanning 23, 36-50. Frosien, J., and Plies, E. (1987). High performance electron optical column for testing ICs with submicrometer design rules. Microelectronic Engineering 7, 163-172. Frosien, J., Plies, E., and Anger, K. (1989). Compound magnetic and electrostatic lenses for low voltage applications. J. Vac. Sci. Technol. B 7, 1874-1877. Gergely, G. (1986). Elastic peak electron spectroscopy. Scanning 8, 203-214. Gergely, G., Menyhfird, M., and Sulyok, A. (1986). Some new possibilities in non-destructive depth profiling using secondary emission spectroscopy: REELS and EPES. Vacuum 36, 471-475. Glaser, W. (1952). Grundlagen der Elektronenoptik. Wien: Springer-Verlag. Gries, W. H., and Werner, W. (1990). Take-off angle and film thickness dependences of the attenuation length of x-ray photoelectrons by a trajectory reversal method. Surf Interf. Anal. 16, 149-153. Gryzinski, M. (1965). Classical theory of atomic collisions. I. Theory of inelastic collisions. Phys. Rev. A 138, 336-358. Hachenberg, O., and Brauer, W. (1959). Secondary electron emission from solids, in Advances in Electronics and Electron Physics, Vol. II, edited by L. Marton. San Diego: Academic Press, pp. 413-499. Hasselbach, F., and Krauss, H.-R. (1988). Backscattered electrons and their influence on contrast in the scanning electron microscope. Scanning Microsc. 2, 1947-1956. Hasselbach, F., and Rieke, U. (1982). Spatial distribution of secondaries released by backscattered electrons in silicon and gold for 20-70 keV primary energy, in Proceedings of the Tenth International Congress on Electron Microscopy, Vol. 1, edited by the Congressional Organization Committee. Hamburg: Deutsche Ges. EM, pp. 253-254. Hawkes, P. W. (1997). Aberrations, in Handbook of Charged Particle Optics, edited by J. Orloff. New York: CRC Press, pp. 223-274. Hawkes, P. W., and Kasper, E. (1996a). Principles of Electron Optics Vol. 2, Applied Geometrical Optics. San Diego: Academic Press. Hawkes, P. W., and Kasper, E. (1996b). Principles of Electron Optics Vol. 3, Wave Optics. San Diego: Academic Press. Hejna, J. (1994). Backscattered electron imaging in low-voltage SEM, in Proceedings of the Thirteenth International Congress on Electron Microscopy, Vol. 1, edited by B. Jouffrey and C. Colliex. Les Ulis, France: Les 6ditions de Physique, pp. 75-76. Hejna, J. (1998). Optimization of an immersion lens design in the BSE detector for the low voltage SEM, in Recent Trends in Charged Particle Optics and Surface Physics Instrumentation, Sixth Seminar, edited by I. Mfillerovfi and L. Frank. Brno: Czechoslovak Society for Electron Microscopy, pp. 30-31. Ho, Y. C., Tan, Z. Y., Wang, X. L., and Chen, J. G. (1991). A theory and Monte Carlo calculation on low-energy electron scattering in solids. Scanning Microsc. 4, 945-951.
SCANNING LEEM
437
Homma, Y., Suzuki, M., and Tomita, M. (1993). Atomic configuration dependent secondary electron emission from reconstructed silicon surfaces. Appl. Phys. Lett. 62, 3276-3278. Huta~, O., Oral, M., Mtillerov/t, I., and Frank, L. (2000). Dimension measurement in a cathode lens equipped low-energy SEM, in Proceedings of the Twelfth European Congress on Electron Microscopy, Vol. 3, edited by L. Frank and F. Ciampor. Brno: Czechoslovak Society for Electron Microscopy, pp. 199-200. Ichimura, S. (1980). Basic study of scanning Auger electron microscopy for surface analysis. Ph.D. Thesis, Osaka University, Japan. Ichinokawa, T., Ishikawa, Y., Kemmochi, M., Ikeda, N., Hosokawa, Y., and Kirschner, J. (1986). Low-energy scanning electron microscopy combined with low-energy electron diffraction. Surface Sci. 176, 397-414. Ichinokawa, T., Ishikawa, Y., Kemmochi, M., Ikeda, N., Hosokawa, Y., and Kirschner, J. (1987). Scanning low-energy electron microscopy. Scanning Microsc. Suppl. 1, 93-97. Ishikawa, Y., Ikeda, N., Kemmochi, M., and Ichinokawa, T. (1985). UHV-SEM observations of cleaning process and step formation on silicon (111) surfaces by annealing. Surface Sci. 159, 256-264. Jacka, M., Kirk, M., E1-Gomati, M. M., and Prutton, M. (1999). A fast, parallel acquisition, electron energy analyzer: The hyperbolic field analyzer. Rev. Sci. Instrum. 70, 2282-2287. Jaklevic, R. C., and Davis, L. C. (1982). Band signatures in the low-energy-electron reflectance spectra for fcc metals. Phys. Rev. B 26, 5391-5397. Joy, D. C. (1984). Beam interactions, contrast and resolution in the SEM. J. Microsc. 136, 241-258. Joy, D. C. (1987). A model for calculating secondary and backscattered electron yields. J. Microsc. 147, 51-64. Joy, D. C. (1989). Control of charging in low-voltage SEM. Scanning 11, 1-4. Joy, D. C. (1995). Monte Carlo Modeling for Electron Microscopy and Microanalysis. Oxford Series in Optical and Imaging Sciences. London: Oxford University Press. Joy, D. C. (2001). A database of electron-solid interactions, Rev. 01-01. http://web.utk.edu/ srcutk/htm/interact.htm. Joy, D. C., and Joy, C. S. (1996). Low voltage scanning electron microscopy. Micron 27, 247-263. Joy, D. C., and Luo, S. (1989). An empirical stopping power relationship for low-energy electrons. Scanning 11, 176-180. Kanaya, K., and Kawakatsu, H. (1972). Secondary electron emission due to primary and backscattered electrons. J. Phys. D: Appl. Phys. 5, 1727-1742. Kanter, H. (1961). Contribution of backscattered electrons to secondary electron formation. Phys. Rev. 121, 681-684. Kato, M., and Tsuno, K. (1990). Numerical analysis of trajectories and aberrations of a Wien filter including the effect of fringing fields. Nucl. Instrum. Meth. Phys. Res. A298, 296-320. Kazumori, H. (2002). Development of JSM-7400F: new secondary electron detection systems permit observation of non-conductive materials. JEOL News 37E(1), 44-47. Khursheed, A. (2002). Aberration characteristics of immersion lenses for LVSEM. Ultramicroscopy 93, 331-338. Kirschner, J. (1984). On the role of the electron spin in scanning electron microscopy, in Scanning Electron Microscopy, Vol. III. edited by O. Johari. Chicago: SEM, pp. 1179-1185. Knell, G., and Plies, E. (1998). Determination of the collection efficiency for combined magnetic-electrostatic SEM objective lenses. Optik 108, 37-42. Kohl, H., Rose, H., and Schnabl, H. (1981). Dose-rate effect at low temperatures in FBEM and STEM due to object heating. Optik 58, 11-24.
438
MfSLLEROV.~ AND FRANK
Kolafik, R., and Lenc, M. (1997). An expression for the resolving power of a simple optical system. Optik 106, 135-139. Kollath, R. (1956). Sekundfirelektronen-Emission fester K6rper bei Bestrahlung mit Elektronen, in Handbuch der Physik, Vol. 21. Berlin: Springer-Verlag, pp. 232-303. Kruit, P., and Lenc, M. (1992). Optical properties of the magnetic monopole field applied to electron microscopy and spectroscopy. J. Appl. Phys. 72, 4505-4513. Kuhr, J.-Ch., and Fitting, H.-J. (1998). Monte-Carlo simulation of low-voltage scanning electron microscopy--LVSEM, in Proceedings of the Fourteenth International Congress on Electron Microscopy, Vol. 1, edited by H.A. Calderon Benavides and M.J. Yacaman. Bristol, UK: Institute of Physics, pp. 451-452. Kuhr, J.-Ch., and Fitting, H.-J. (1999). Monte Carlo simulation of electron emission from solids. J. El. Spectrosc. Rel. Phenom. 105, 257-273. Kulenkampff, H., and Spyra, W. (1954). Energieverteilung rtickdiffundierter Elektronen. Z. Phys. 137, 416-425. Le Gressus, C., Valin, F., Gautier, M., Duraud, J. P., Cazaux, J., and Okuzumi, H. (1990). Charging phenomena on insulating materials: mechanisms and applications. Scanning 12, 203-210. Lenc, M. (1995). Immersion objective lenses for very low energy electron microscopy, in Proceedings of the Multinational Congress on Electron Microscopy, edited by F. Ciampor. Bratislava: Slovak Academic Press, pp. 103-104. Lenc, M., and Mtillerovfi, I. (1992a). Electron optical properties of a cathode lens. Ultramicroscopy 41, 411-417. Lenc, M., and Mtillerovfi, I. (1992b). Optical properties and axial aberration coefficients of the cathode lens in combination with a focusing lens. Ultramicroscopy 45, 159-162. Lencovfi, B. (1997). Electrostatic lenses. Handbook of Charged Particle Optics, edited by J. Orloff. New York: CRC Press, pp. 177-221. Lencovfi, B., and Wisselink, G. (1990). Program package for the computation of lenses and deflectors. Nucl. Instrum. Meth. A298, 56-66. Libinson, A. G. (1999). Tilt dependence of secondary electron emission at low excitation energy. Scanning 21, 23-26. Liebel, H., and ~Senftinger, B. (1991). Low-energy electron microscope of novel design. Ultramicroscopy 36, 91-98. Llacer, J., and Garwin, E. L. (1969). Electron-phonon interaction in alkali halides~I. The transport of secondary electrons with energies between 0.25 and 7.5 eV. J. Appl. Phys. 40, 2766-2775. Mankos, M., and Adler, D. (2002). Electron-electron interactions in cathode objective lenses. Ultramicroscopy 93, 347-354. Martin, J. P., Weimer, E., Frosien, J., and Lanio S. (1994). Ultra-high resolution SEM--A new approach. Microscopy and Analysis (USA), March, 19. McKernan, S. (1998). A comparison of detectors for low voltage contrast in the SEM, in Proceedings of the Fourteenth International Congress on Electron Microscopy, Vol. 1, edited by H. A. Calderon Benavides and M. J. Yacaman. Bristol, UK: Institute of Physics, pp. 481-482. Meisburger, W. D., Brodie, A. D., and Desai, A. A. (1992). Low-voltage electron-optical system for the high-speed inspection of integrated circuits. J. Vae. Sci. Technol. B 10, 2804-2808. Miyoshi, M., Yamazaki, Y., Nagai, T., and Nagahama, I. (1999). Development of a projection imaging electron microscope with electrostatic lenses. J. Vac. Sci. Technol. B 17, 2799-2802. Morin, P., Pitaval, M., and Vicario, E. (1976). Direct observation of insulators with a scanning electron microscope. J. Phys. E: Sci. Instrum. 9, 1017-1020.
SCANNING LEEM
439
Mott, N. F., and Massey, H. S. W. (1965). The Theory of Atomic Collisions. London: Oxford University Press. Mfillerovfi, I. (1996). Contrast mechanisms in low voltage SEM, in Proceedings of the Ninth Conference on Electron Microscopy of Solids, edited by A. Czyrska-Filemonowicz. Krak6w: State Committee for Scientific Research, pp. 93-96. Mfillerov~, I. (2001). Imaging of specimens at optimized low and very low energies in scanning electron microscopes. Scanning 23, 379-394. Mfillerovfi, I., and Frank, L. (1993). Very low energy microscopy in commercial SEMs. Scanning 15, 193-201. Mfillerov~, I., and Frank, L. (1994). Use of cathode lens in scanning electron microscope for low voltage applications. Mikrochim. Acta 114/115, 389-396. Mfillerovfi, I., and Frank, L. (2002). Practical resolution limit in the scanning lowenergy electron microscope, in Proceedings of the Fifteenth International Congress on Electron Microscopy, Vol. 3, edited by R. Cross, J. Engelbrecht, T. Sewell, M. Witcomb, and P. Richards. Onderstepoort: Microscopy Society of Southern Africa, pp. 99-100. Mfillerovfi, I., and Frank, L. (2003). Contrast at very low energies of the gold/carbon specimen for resolution testing. Scanning, submitted. Mfillerovfi, I., and Lenc, M. (1992a). Some approaches to low-voltage scanning electron microscopy. Ultramicroscopy 41, 399-410. Mfillerov~, I., and Lenc, M. (1992b). The scanning very-low-energy electron microscope (SVLEEM). Mikrochim. Acta (Suppl.) 12, 173-177. Mfillerov~t, I., E1-Gomati, M. M., and Frank, L. (2002). Imaging of the boron doping in silicon using low-energy SEM. Ultramicroscopy 93, 223-243. Mfillerovfi, I., Frank, L., and HutaL O. (2001). Visualization of the energy band contrast in SEM through low-energy electron reflectance. Scanning 23, 115. Mfillerovfi, I., Lenc, M., and Florifin, M. (1989). Collection of backscattered electrons with a single polepiece lens and a multiple detector. Scanning Microsc. 3, 419-428. Mfillerov~, I., Zadra~il, M., and Frank, L. (1997). Low-energy SEM imaging of bevelled multilayers. J. Comput. Assist. Microsc. 9, 121-122. Mulvey, T. (1984). Magnetic electron lenses II, in Electron Optical Systems for Microscopy, Microanalysis and Microlithography, edited by J. J. Hren, F. A. Lenz, E. Munro, and P. B. Sewell. Chicago: SEM, pp. 15-27. Nagatani, T., Saito, S., Sato, M., and Yamada, M. (1987). Development of an ultrahigh resolution SEM by means of a field emission source and in-lens system. Scanning Microsc. 1, 901-909. Nieminen, R. M. (1988). Stopping power for low-energy electrons. Scanning Microsc. 2, 1917-1926. Ono, S., and Kanaya, K. (1979). The energy dependence of secondary emission based on the range-energy retardation power formula. J. Phys. D: Appl. Phys. 12, 619-632. Paden, R. S., and Nixon, W. C. (1968). Retarding field scanning electron microscopy. J. Phys. E: Sci. Instrum. 1, 1073-1080. Pawley, J. B. (1984). Low voltage scanning electron microscopy. J. Microsc. 136, 45-68. Pejchl, D., Mfillerov~, I., and Frank, L. (1993). Unconventional imaging of surface relief. Czech. J. Phys. 43, 983-992. Pejchl, D., Mfillerov~, I., Frank, L., and Kolafik, V. (1994). Separator of primary and signal electrons for very-low-energy SEM. Czech. J. Phys. 44, 269-276. Penn, D. R. (1987). Electron mean free path calculations using a model dielectric function. Phys. Rev. B 35, 482-486.
440
MULLEROVA AND FRANK
Pfefferkorn, G. E., Gruter, H., and Pfautsch, M. (1972). Observations on the prevention of specimen charging, in Scanning Electron Microscopy, Vol. I, edited by O. Johari. Chicago: SEM, pp. 147-152. Plies, E., Degel, B., Hayn, A., Knell, G., and Schiebel, B. (1998). Experimental results using a "low-voltage booster" in a conventional SEM, in Proceedings of the Fifth International Conference on Charged Particle Optics, edited by P. Kruit and P. W. van Amersfoort. Amsterdam: Elsevier, pp. 126-130. Powell, C. J. (1974). Attenuation lengths of low-energy electrons in solids. Surface Sci. 44, 29-46. Powell, C. J. (1984). Inelastic mean free paths and attenuation lengths of low-energy electrons in solids, in Scanning Electron Microscopy, Vol. IV, edited by O. Johari. Chicago: SEM, pp. 1649-1664. Powell, C. J. (1985). Calculations of electron inelastic mean free paths from experimental optical data. Surf Interf. Anal. 7, 263-274. Powell, C. J. (1987). The energy dependence of electron inelastic mean free path. Surf Interf. Anal. 10, 349-354. Preikszas, D., and Rose, H. (1995). Procedures for minimizing the aberrations of electromagnetic compound lenses. Optik 100, 179-187. Price, C. W., and McCarthy, P. L. (1988). Low voltage scanning electron microscopy of lowdensity materials. Scanning 10, 29-36. Rao-Sahib, T. S., and Wittry, D. B. (1974). X-ray continuum from thick element targets for 1050 keV electrons. J. Appl. Phys. 45, 5060-5068. Recknagel, A. (1941). Theorie des elektrischen Elektronenmikroskops fiir Selbststrahler. Z. Phys. 117, 689-708. Reimer, L. (1971). Rauschen der Sekundfirelektronenemission. Beitr(ige Elektr. Direktabb. Oberfldichen (BEDO) 412, 299-304. Reimer, L. (1995). In Energy-Filtering Transmission Electron Microscopy, edited by L. Reimer. Berlin: Springer-Verlag, pp. 7-9. Reimer, L. (1996). MOCASIM--Ein Monte Carlo Programm ffir Forschung und Lehre. Beitr. Elektr. Mikr. Direktabb. Oberfl. (BEDO) 29, 1-10. Reimer, L. (1998). Scanning Electron Microscopy. Berlin: Springer-Verlag. Reimer, L., and Kfissens, M. (1994). Application of a two-detector system for secondary and backscattered electrons in LVSEM, in Proceedings of the Thirteenth International Congress on Electron Microscopy, Vol. 1, edited by B. Jouffrey and C. Colliex. Les Ulis, France: Les 6ditions de Physique, pp. 73-74. Reimer, L., and Wfichter, M. (1978). Contribution to the contamination problem in TEM. Ultramicroscopy 3, 169-174. Reimer, L., B6ngeler, R., K~issens, M., Liebscherr, F. F., and Senkel, R. (1991). Calculation of energy spectra from layered structures for backscattered electron spectrometry and relations to Rutherford backscattering spectrometry by ions. Scanning 13, 381-391. Reimer, L., Golla, U., B6ngeler, R., Kfissens, M., Schindler, B., and Senkel, R. (1992). Charging of bulk specimens, insulating layers and free supporting films in scanning electron microscopy. Optik 92, 14-22. Reimer, L., and L6dding, B. (1984). Calculation and tabulation of Mott cross-sections for large-angle scattering. Scanning 6, 128-151. Reimer, L., and Tollkamp, C. (1980). Measuring the backscattering coefficient and secondary electron yield inside a SEM. Scanning 8, 35-39. Rose, H. (1987). The retarding Wien filter as a high-performance imaging filter. Optik 77, 26-34. Rose, H., and Preikszas, D. (1992). Outline of a versatile corrected LEEM. Optik 92, 31-44.
SCANNING LEEM
441
Rose, H., and Spehr, R. (1980). On the theory of the Boersch effect. Optik 57, 339-364. Salehi, M., and Flinn, E. A. (1981). Dependence of secondary electron emission from amorphous materials on primary angle of incidence. J. Appl. Phys. 52, 994-996. Sato, M., Todokoro, H., and Kageyama, K. (1993). A snorkel type objective lens with E x B field for detecting secondary electrons. SPIE 2014, 17-23. Schfifer, J., and H61zl, J. (1972). A contribution to the dependence of secondary electron emission from the work function and Fermi energy. Thin Solid Films 18, 81-86. Schauer, P., and Autrata, R. (1998). Computer optimized design of BSE scintillation detector for SEM, in Proceedings of the Eleventh European Congress on Electron Microscopy, Vol. I, edited by Committee of European Societies for Microscopy. Brussels: CESM, pp. 369-370. Schmid, R., and Brunner, M. (1986). Design and application of a quadrupole detector for lowvoltage scanning electron microscopy. Scanning 8, 294-299. Schmid, R., Gaukler, K.H., and Seiler, H. (1983). Measurement of elastically reflected electrons (E _<2.5 keV) for imaging of surfaces in a simple ultra high vacuum scanning electron microscope, in Scanning Electron Microscopy, Vol. II, edited by O. Johari. Chicago: AMF O'Hare, pp. 501-509. Schreiber, E., and Fitting, H.-J. (2002). Monte Carlo simulation of secondary electron emission from the insulator SiO2. J. El. Spectrosc. Rel. Phenom. 124, 25-37. Seah, M. P., and Dench, W. A. (1979). Quantitative electron spectroscopy of surfaces: a standard database for electron inelastic mean free paths in solids. Surf Interf. Anal. 1, 1-11. Sealy, C. P., Castell, M. R., and Wilshaw, P. R. (2000). Mechanism for secondary electron dopant contrast in the SEM. J. El. Microsc. 49, 311-321. Seiler, H. (1967). Some problems of secondary electron emission. Z. Angew. Physik 22, 249-263. Seiler, H. (1983). Secondary electron emission in the scanning electron microscope. J. Appl. Phys. 54, R l-R18. Seiler, H., and Kuhnle, G. (1970). Anisotropy of the secondary electron yield as a function of the energy of the primary electrons from 5 to 20 keV. Z. Angew. Physik 29, 254-260. Shaffner, T. J., and Van Veld, R. D. (1971). "Charging" effects in the scanning electron microscope. J. Phys. E: Sci. Instrum. 4, 633-637. Shao, Z. (1989). Extraction of secondary electrons in a newly proposed immersion lens. Rev. Sci. Instrum. 60, 693-699. Spehr, R. (1985). Broadening of charged particle microprobes by stochastic Coulomb interactions. Optik 70, 109-114. Strocov, V. N., and Starnberg, H. I. (1995). Absolute band-structure determination by target current spectroscopy: Application to Cu(100). Phys. Rev. B 52, 8759-8765. Strocov, V. N., Starnberg, H. I., Nilsson, P. O., and Holleboom, L. J. (1996). Determining unoccupied bands of layered materials by VLEED: implications for photoemission band mapping. J. Phys.. Condens. Matter 8, 7549-7559. Takashima, S. (1994). New electron optical technologies in low voltage scanning electron microscope. JEOL News 31E(1), 33-35. Tanuma, S., Powell, C. J., and Penn, D. R. (1991a). Calculations of electron inelastic mean free paths II. Data for 27 elements over the 50-2000 eV range. Surf Interf. Anal. 17, 911-926. Tanuma, S., Powell, C. J., and Penn, D. R. (1991b). Calculations of electron inelastic mean free paths III. Data for 15 inorganic compounds over the 50-2000 eV range. Surf Interf. Anal. 17, 927-939. Telieps, W. (1987). Surface imaging with LEEM. Appl. Phys. A 44, 55-61. Telieps, W., and Bauer, E. (1985). An analytical reflection and emission UHV surface electron microscope. Ultramieroscopy 17, 57-66. Thomas, S., and Pattinson, E. B. (1970). Range of electrons and contribution of back-scattered electrons in secondary production in aluminum. J. Phys. D: Appl. Phys. 3, 349-357.
442
M[ILLEROV,~i AND FRANK
Tromp, R. M. (2000). Low-energy electron microscopy. IBM J. Res. Develop. 44, 503-516. Tromp, R. M., and Reuter, M. C. (1993). Imaging with a low-energy electron microscope. Ultramicroscopy 50, 171-178. Tromp, R. M., Denier van der Gon, A. W., LeGoues, F. K., and Reuter, M. C. (1993). Observation of buried interfaces with low-energy electron microscopy. Phys. Rev. Lett. 71, 3299-3302. Tsai, F. C., and Crewe, A. V. (1998). A gapless magnetic objective lens for low voltage SEM. Optik 109, 5-11. Tung, C. J., Ashley, J. C., and Ritchie, R. H. (1979). Electron inelastic mean free paths and energy losses in solids, II. Electron gas statistical model. Surface Sci. 81, 427-439. Veneklasen, L. H. (1992). The continuing development of low-energy electron microscopy for characterizing surfaces. Rev. Sci. Instrum. 63, 5513-5532. Welter, L. M., and McKee, A. N. (1972). Observations on uncoated, nonconducting or thermally sensitive specimens using a fast scanning field emission source SEM, in Scanning Electron Microscopy, Vol. I, edited by O. Johari. Chicago: SEM, pp. 161-166. Werner, W. S. M. (1992). The role of the attenuation parameter in electron spectroscopy. J. El. Spectrosc. Rel. Phenom. 59, 275-291. Werner, W. S. M. (1996). Transport equation approach to electron microbeam analysis: fundamentals and applications. Mikrochim. Acta (Suppl.) 13, 13-38. Woodruff, D. P., and Delchar, T. A. (1986). Modern Techniques of Surface Science. Cambridge: Cambridge University Press. Ximen, J., Lin, P. S. D., Pawley, J. B., and Schippert, M. (1993). Electron optical design of a high-resolution low-voltage scanning electron microscope with field emission gun. Rev. Sci. Instrum. 64, 2905-2910. Yau, Y. W., Pease, R. F. W., Iranmanesh, A. A., and Polasko, K. J. (1981). Generation and applications of finely focused beams of low-energy electrons. J. Vac. Sci. Technol. 19, 1048-1052. Zach, J. (1989). Design of a high-resolution low-voltage scanning electron microscope. Optik 83, 30-40. Zach, J., and Haider, M. (1992). A high-resolution low voltage scanning electron microscope, in Proceedings of the Tenth European Congress on Electron Microscopy, Vol. 1, edited by A. Rios, J.M. Arias, L. Megias-Megias, and A. Lopez-Galindo. Granada: Univ. de Granada, pp. 49-53. Zach, J., and Rose, H. (1986). Efficient detection of secondary electrons in low-voltage scanning electron microscopy. Scanning 8, 285-293. Zach, J., and Rose, H. (1988). High-resolution low-voltage electron microprobe with large SE detection efficiency, in Proceedings of the Ninth European Congress on Electron Microscopy, Vol. l, edited by P.J. Goodhew and H.G. Dickinson. Bristol, UK: Institute of Physics, pp. 81-82. Zadra~il, M., E1-Gomati, M. M., and Walker, A. (1997). Measurements of very-low-energy secondary and backscattered electron coefficients. J. Comput. Ass. Microsc. 9, 123-124. Zadra~il, M., and E1-Gomati, M. M. (1998a). Measurements of the secondary and backscattered electron coefficients in the very-low-energy range, in Recent Trends in Charged Particle Optics and Surface Physics Instrumentation, Sixth Seminar, edited by I. Miillerov~ and L. Frank. Brno: Czechoslovak Society for Electron Microscopy, p. 82. Zadra~il, M., and E1-Gomati, M. M. (1998b). Measurements of the secondary and backscattered electron coefficients in the energy range 250-5000 eV, in Proceedings of the Fourteenth International Congress on Electron Microscopy, Vol. l, edited by H.A. Calderon Benavides and M.J. Yacaman. Bristol, UK: Institute of Physics, pp. 495-496. Zadra~il, M., and E1-Gomati, M. M. (2002). Unpublished data.
SCANNING LEEM
443
Zoba6ovfi, J., and Frank, L. (2003). Specimen charging and detection of signal from nonconductors in a cathode lens equipped SEM. Scanning, 25, 150-156. Zoba~ovfi, J., Oral, M., Huta~, O., Mtillerovfi, 2., and Frank, L (2003). Corrections of magnification and focusing in a cathode lens equipped SEM. To be submitted. Zworykin, V. A., Hillier, J., and Snyder, R. L. (1942). A scanning electron microscope. A S T M Bull. 117, 15-23.
Scanning Low-Energy Electron Microscopy ILONA MULLEROV/i~ and LUDI~K FRANK Institute of Scientific Instruments AS CR, Krdtlovopolskdt 147, CZ-61264 Brno, Czech Republic
I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. M o t i v a t i o n s to L o w e r the E l e c t r o n E n e r g y . . . . . . . . . . . . . . . . . . . . . A. E x t e n s i o n s to C o n v e n t i o n a l M o d e s of O p e r a t i o n . . . . . . . . . . . . . . . B. N e w O p p o r t u n i t i e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Issues I n h e r e n t to Slow E l e c t r o n B e a m s . . . . . . . . . . . . . . . . . . . . III. I n t e r a c t i o n of Slow E l e c t r o n s w i t h Solids . . . . . . . . . . . . . . . . . . . . . . A. Elastic S c a t t e r i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. S c a t t e r i n g on N u c l e i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Reflection o n E n e r g y G a p s . . . . . . . . . . . . . . . . . . . . . . . . . . B. Inelastic S c a t t e r i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. S c a t t e r i n g o n E l e c t r o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Scattering o n A t o m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. P e n e t r a t i o n o f Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. H e a t i n g a n d D a m a g e of the S p e c i m e n . . . . . . . . . . . . . . . . . . . . . E. S p e c i m e n C h a r g i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. T o o l s for S i m u l a t i o n o f E l e c t r o n Scattering . . . . . . . . . . . . . . . . . . IV. E m i s s i o n o f E l e c t r o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. E l e c t r o n B a c k s c a t t e r i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. C r y s t a l l i n i t y Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. C o h e r e n c e w i t h i n the P r i m a r y B e a m S p o t . . . . . . . . . . . . . . . . . . . D. S e c o n d a r y E l e c t r o n E m i s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . V. F o r m a t i o n o f the P r i m a r y B e a m . . . . . . . . . . . . . . . . . . . . . . . . . . A. T h e S p o t Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. I n c o r p o r a t i o n o f the R e t a r d i n g Field . . . . . . . . . . . . . . . . . . . . . . C. T h e C a t h o d e L e n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. T h e Pixel Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. S p u r i o u s Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Testing the R e s o l u t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. D e t e c t i o n a n d S p e c i m e n - R e l a t e d Issues . . . . . . . . . . . . . . . . . . . . . . . A. D e t e c t i o n Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. D e t e c t o r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Signal C o m p o s i t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. S p e c i m e n Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. S p e c i m e n Tilt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
310 314 314 316 317 319 320 320 323 324 324 328 331 334 336 340 343 345 350 353 354 361 362 366 369 374 377 379 381 382 387 393 394 397
VII. I n s t r u m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A d a p t a t i o n o f C o n v e n t i o n a l S E M s . . . . . . . . . . . . . . . . . . . . . . . B. D e d i c a t e d E q u i p m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. A l i g n m e n t a n d O p e r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . .
399 399 401 407
309 Copyright 9 2003 Elsevier Inc. All rights reserved. 1076-5670/2003 $35.00
310
MULLEROVA AND FRANK
D. Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Selected Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Prospective Application Areas. . . . . . . . . . . . . . . . . . . . . . . . . . B. General Characteristics of Micrograph Series . . . . . . . . . . . . . . . . . C. Surface Relief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Critical Energy Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Diffraction Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Contrast of Crystal Orientation . . . . . . . . . . . . . . . . . . . . . . . . . G. Layered Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Material Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Electronic Contrast in Semiconductors . . . . . . . . . . . . . . . . . . . . . J. Energy-Band Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
410 413 414 415 417 418 419 422 422 425 426 430 431 432 432
I. INTRODUCTION Two versions of the electron microscope, the directly imaging (usually T E M , transmission electron microscope) and scanning (SEM) models, have coexisted in the instrument market and in laboratories for decades and none of them seems likely to lose ground. At certain periods, one or the other attracts enhanced attention and makes a more significant step forward, leaving afterwards the m o m e n t a r y leadership to the competing principle. A period rich in innovations has been experienced by SEM designers and brought two successful novelties, namely the environmental SEM with the specimen surrounded by a gas at a pressure of thousands of Pa and high-resolution imaging at electron beam energies down to fractions of eV. Our purpose here is to review the theoretical and practical aspects of the latter and to present the method as being already fully feasible and worth employing in the majority of SEM application areas. The term "low-energy" electron is obviously of a qualitative nature and should be given some quantitative limits. This limit could be best based on characteristics of the electron interaction with solids that provides the image signal in SEM. Examining the typical energy dependences of all relevant quantities connected with this interaction, we can find good reasons for the definition of two such energy intervals instead of only one. Figure 1 shows the atomic number dependence of the so-called second critical energy Ec2, i.e., the higher of two electron impact energies at which the total electron emission yield is equal to one (or to 100%). These energies exist for nearly all solids with a few exceptions such as conductors of lowest mean atomic numbers, for which the total emission does not exceed the unit level. Above Ec2 the electron emission decreases monotonically and no thresholds can be
SCANNING LEEM
311
6 O
Ec2 [keY] 4
O
. . . . . . . . . . . . . . . . . .
J .
_ .O . . . . . . . . . . . . . . . . . . . . . .
o
o
8
0
o
o~
o
oo q~
2
.............
o
O ....................
0
0 , ~
'0
0
~
0
o ~ 0
o ,
.............................................................
20
........
0
40 60 atomic number
, ......
,,,,,,,
.......
,~ . . . .
80
FIGURE 1. The higher of the critical energies for normal electron impact, Ec2, at which the total electron yield is equal to one, plotted versus the atomic number for conductive chemical elements; data were collected from Bauer and Seiler (1984) and Zadra~il and E1-Gomati (2002). identified. On the contrary, the energy Ec2 alone represents a significant breakpoint at which the specimen charging changes its sign. As the graph shows, a value like 5 keV can be taken as a margin of this interval. Thus, let us consider the "low-energy" range below 5 keV beam energy. As will be shown subsequently, around this threshold the yield of backscattered electrons (BSE) also loses its monotonic dependence on the atomic number, which exists at higher energies, so that the conventional material contrast ceases to be reliably usable. In Figure 2, the well-known plot of the inelastic mean free path (IMFP) of electrons is shown versus energy for numerous elements and compounds. The deep minimum at approximately 50 eV represents another crucial threshold: the I M F P starts to grow below this point because the main interaction phenomena, the secondary electron (SE) emission in particular, settle here and a fundamentally new situation emerges for the scanned imaging. So let us define also the "very low energy" interval below 50 eV. Later we will see that this energy range can be further subdivided but this would miss its practical purpose. The commercial SEM instruments traditionally used primary beam energies of 15-30 keV as a compromise between sufficiently small spot size and reasonable SE emission. The series of preadjusted beam energies in SEM mostly ended at 5 keV and when even lower energies were possible, good-quality micrographs were not acquired. Progress in the computeraided design methods for electron optics opened ways to tailoring the objective lenses and even full columns to desired parameters and afterwards the SEM instruments entered the low-energy range down to about 1 keV.
312
MLTLLEROYA AND FRANK '~
' I"'lli'illll
'i
i Ililili ....... '1 I I'11'11|1" I I iI~_
E - E,, (eV)
FIGURE 2. The energy dependence of the inelastic mean free path of electrons; the dots represent various elements and compounds. (Reprinted with permission from Seah and Dench, 1979.) The motivation included the suppressed charging and better visualization of surface relief details that projected itself, among others, into more precise measurement of distances in the images. This experience made the lowenergy range known and acceptable for the community of microscopists but no trends to push the energy further down have been apparent albeit possible sources of motivation existed for a long time in experimental areas adjacent to SEM. The so-called emission electron microscope (EEM) is in fact one of the oldest versions of EM. In this type of directly imaging microscope the specimen itself is the source of electrons, which are emitted under excitations that include impact of photons, electrons and/or ions or high-temperature heating. More than 60 years ago Recknagel (1941) published a theoretical study showing that the immersion objective lens, a crucial part of EEM that accelerates the electrons emitted at quite low energy E0 to some final energy E and forms the first image of the emitting surface, has surprisingly good properties. Its basic aberration coefficients are proportional to the ratio Eo/E so that they decrease even for the lowest emission energies. Of the EEM versions mentioned, the photoemission one (PEEM) is most often met in laboratories at present, partly because of the progress in this method, connected with extended availability of intensive radiation sources at synchrotrons. However, for us another version of the EEM is most important, namely the low-energy electron microscope (LEEM), in which the specimen excitation is made via a parallel coherent wave of slow
SCANNING LEEM
313
electrons. The method and instrument were first proposed by Bauer (1962) and demonstration experiments were later performed by Delong and Drahog (1971). Only in the 1980s did the first micrographs appear in the literature (Telieps and Bauer, 1985) but since then the method boomed; for a review see Bauer (1994), while more practical aspects are summarized by Veneklasen (1992). Although the LEEM apparatus remains an expensive tool for top specialists, it produced the most attractive and fruitful results from among the surface examination methods except, maybe, probe microscopies. The scanning LEEM (SLEEM) method described here aims at achieving similar results as regards observability of surface-localized physical phenomena, with possibilities of extension toward multiple signal detection. The idea of reversing the function of the immersion objective lens with respect to that in EEM can be originally found in Zworykin et al. (1942) where an electrostatic SEM with biased specimen is outlined. Adaptation to a conventional SEM, by inserting a retarding field element below its objective lens, was published by Paden and Nixon (1968). Yau et al. (1981) demonstrated lowering of the aberration coefficients by means of a retarding field, either overlapped over the focusing magnetic field or arranged sequentially, and even measured the aberration coefficients down to tens of gm at very low energies but their aim was solely to improve tools for electron lithography and annealing and they did not consider any application to scanned low-energy imaging. Many other attempts to retard the primary beam electrons before their impact onto the specimen were published and this history is reviewed by Mtillerovfi and Lenc (1992a). It is interesting that, although many of the previous studies proposed quite feasible solutions to the problem of decelerating the beam in SEM, none of the reviewed papers presented convincing results, i.e., micrographs collected throughout the full energy scale. To our knowledge, the first such series was published by us (Mtillerovfi and Frank, 1993) together with practical experience from adaptation of a commercial SEM to the SLEEM method. The low-energy microscopy program at ISI Brno was started in the 1960s (see above) and after a long break it continued with the first demonstration experiments with the SLEEM method (Mtillerovfi and Lenc, 1992b) and theoretical examination of properties of the immersion objective lens (IOL) (Lenc and Mfillerovfi, 1992a,b). The problem of IOL and its optimization was systematically treated by Rose and Preikszas (1992) and Preikszas and Rose (1995). More literature references will be given below. One could easily conclude that the method and Corresponding apparatus have been sufficiently explored to appear on the instrument market and to
314
MULLEROVA AND FRANK
enter the broad community of users. Moreover, the method may be launched after quite moderate adaptation to a conventional SEM. Nevertheless, the small number of existing instruments corresponds to only a handful of users, who do not represent a sufficient marketing target, so that the barrier has not been broken yet. The first commercial device is expected in 2003. In the following the SLEEM method will be discussed in detail from all fundamental viewpoints so that the reader can comprehend it and even start to use it. The scope of the application results is still quite limited and awaits additional users who could contribute to filling the obscure areas in the interpretation of the contrast observed.
II. MOTIVATIONS TO LOWER THE ELECTRON ENERGY The low-energy range below 5 keV is now available in commercial SEM instruments and widely used, for observation of nonconductors, for measurement of dimensions in images, for improved observation of surface relief, etc. In this chapter we will summarize the main advantages of working in this energy range and then continue with the very-lowenergy range. Let us mention here that practical experience with image contrast (and therefore also the awareness of motivation for using it) is quite naturally concentrated mainly in the energy ranges of commercial instruments. These mostly provide quality imaging down to 1 keV where the resolution value is often still guaranteed. Somewhere below 1 keV the imaging properties "break down" and the image quality becomes unacceptable--this threshold is usually met around 500 eV. For microscopes containing compound objective lenses, this limit is shifted to about 200 eV and the performance of devices equipped with an aberration corrector is similar.
A. Extensions to Conventional Modes of Operation 9 It is well known (and also evident from Figures 13 and 16) that the total electron yield a per incident electron, acquired from any known specimen, increases when the primary beam energy is reduced below its usual value of 15 to 30 keV. This is because of shrinkage of the interaction volume together with the path of generated secondary electrons towards the surface, which reduces absorption. Because a is generally less than 1 at high energies, its increase leads to a decrease in the portion of electrons dissipated in the specimen, suppression of
SCANNING LEEM
9 9
9
9
9
9
9
315
charging of nonconductive specimens, and lesser demands on requirements to make them conductive. At the critical energy Ec2 we get ~r= 1 and a true noncharging microscopy is possible (Frank and Mtillerov~t, 1994). As the SE yield 6 keeps growing even when below Ec2, a significant signal increase with respect to the traditional beam energies is achieved, which projects itself into improved signal-to-noise ratio (SNR) in the image. Measurements on elemental specimens showed that the SE signal maximum appears at energy Em between 100 and 800 eV (e.g., Seiler, 1983) and below this energy the yield again falls. The so-called material contrast, based on direct proportionality between the mean atomic number of the specimen and the yield 7/of backscattered electrons, which is reliably available at tens of keV, disappears in the low energy range in the sense that the r/(E) curves for various specimens start to cross each other (see Figure 13). Instead, for particular combinations of materials, optimum energies can be found at which the mutual contrast reaches its maximum (see Mfillerovfi, 2001). As the interaction volume of slower electrons diminishes, information generated in the microscope becomes better localized and more sensitive to the true surface, which is then also more truly visualized. Tiny protrusions and ridges appear on facets that were apparently smooth at higher beam energies. The so-called edge effect, i.e., overbrightening of steeply inclined facets or side walls of surface steps that is apparent and mostly dominant at tens of keV, diminishes here and fully disappears somewhere below 500 eV (in fact near Em for the maximum SE yield). The reason is that the penetration depth of primary electrons (PE) shortens and approaches the escape depth of SE. Consequently, all generated SE are emitted and no surface steps can extend the emitting area. Experience has shown that, in the range of hundreds of eV, a contrast between various grains appears on polycrystalline specimens. This phenomenon needs to be explored more carefully because in principle there are several possible explanations: in addition to dependence of both the generation and absorption of SE and of the electron backscattering on the crystal orientation, the presence of thin surface films can also play a role as these layers cease to be transparent here and their thickness (like that of oxides) is also orientation dependent. The energy dissipation in the specimen is clearly smaller at low energies--each electron delivers less energy. The increase in emission of slow SE makes no significant change and the BSE emission, which is responsible for the great majority of the energy export, is roughly
316
MOLLEROVA AND FRANK
constant down to hundreds of eV (see Figure 13). Nevertheless, at higher energies and still at 1 keV the penetration depth (or electron range) decreases faster than linearly (see B6ngeler et al., 1993) so that the spatial density of dissipated energy grows. Then this decrease gradually becomes linear (Joy and Joy, 1996) and the density of dissipated energy stays constant because the deficit in the energy income is just compensated with thinning of the interaction layer. 9 The question of radiation damage is even more complicated than the previous issue. In addition to changes in the total amount of dissipated energy and in its spatial density, the cross-sections for various inelastic phenomena also depend on the energy of incident electrons. For example, cracking of hydrocarbon molecules and creation of the contamination graphitic layer is most effective for electron impact at about 100 to 200 eV. Only in the very-low-energy range do the elastic collisions dominate and the radiation damage diminishes and disappears.
B. New Opportunities
9 In the very-low-energy range, the wavelength of incident electrons, )~ [nm]= 1.226 x {E[eV]} -1/2, becomes comparable with the interatomic distances. As in the classical LEED (low-energy electron diffraction) apparatus, the angular distribution of the reflected electrons is strongly anisotropic and the intensity is concentrated into diffracted beams. In our case, the incident wave is convergent and one can refer to the CBED (convergent beam electron diffraction) method used in the STEM (scanning transmission electron microscope). Selective detection of some diffracted beams enables one to directly visualize the surface crystallinity and its possible changes. 9 Flat clean crystal surfaces are composed of terraces that are smooth on the atomic level and separated by steps of a height of one or more atoms. If the primary spot illuminates a terrace margin and the electron wavelength is in suitable relation to the step height, the two parts of the wavefront, reflected on adjacent terraces, can interfere (the dividedwavefront interference) constructively or destructively and reveal the step although the point resolution of the microscope does not reach the atomic level. 9 A similar phenomenon can be observed when the interference concerns electrons reflected from upper and lower interfaces of a thin surface film (the divided-amplitude interference). At wedge-shaped layers,
SCANNING LEEM
9
9
9
9
317
equal-thickness stripes (an analogy to Newton's rings) should be observed. Electrons impacting the solid with energy just above the surface potential barrier are, according to laws of quantum mechanics, subject to partial reflection so that the height and shape of the barrier can be sensed. It is known from LEED experiments that the electron reflection (Bauer, 1994; Barto~ et al., 1996) is inversely proportional to the local density of electron states coupled to the incident wave. This phenomenon can appear only below 20 or 30 eV of landing energy. The contrast based on the local density of states enables one to directly observe the energy band structure, which opens ways to attractive applications, e.g., in development and diagnostics of semiconductor structures (Frank et al., 2002; Mfillerov~ et al., 2002). Already in the low-energy range (and especially for heavier specimens), the elastic electron scattering displays behavior that can be described solely by the quantum mechanical Mott cross-sections, which incorporate screening of the nucleus by electrons, existence of the spin, and the spin-orbital interaction (see, e.g., Reimer, 1998). Thus, the electron spin influences the image signal and the magnetic microstructure becomes observable provided a spin-polarized beam is used for the illumination (Bauer, 1994). As mentioned above, below about 20 to 30 eV elastic collisions of incident electrons start to dominate so that radiation damage becomes negligible. This can be important for examination of highly sensitive materials and also, for example, for interoperational checks in semiconductor production where any damage should be avoided.
C. Issues Inherent to Slow Electron Beams
Problems with the generation of sufficiently small electron probes in the lowenergy range have been solved reasonably satisfactorily and these beam energies are available in modern instruments. Nevertheless, the low-energy range has been explored only down to about 200 eV, as already noted. Let us now summarize the problems that have to be overcome when lowering the beam energy with an instrument having this energy constant throughout the microscope column. 9 The chromatic aberration of electron lenses depends on the ratio A E / E , where the energy spread AE within the beam is given by the emission mechanism used in the gun and E is the beam energy within the lens.
318
9
9
9
9
9
9
MOLLEROVAAND FRANK Obviously, the chromatic aberration disc enlarges with decreasing energy and in the low-energy range it usually dominates as regards the image resolution and affects this crucial characteristic adversely. The diffraction aberration, i.e., the size of the Airy disc arising from interference of the unscattered electron wave, passing through the aperture-restricting diaphragm, with the marginal wave scattered on the diaphragm edge, is proportional to the wavelength ~, i.e., to E -1/2. Thus, this contribution to the final spot size also grows at low energies. The electron current extracted from the gun is proportional to the extraction voltage. For thermionic cathodes, the gun brightness is linearly proportional to E (Reimer, 1998). For Schottky- and fieldemission guns, this proportionality is not so simple because the first acceleration voltage controls the emission and the final beam energy is adjusted afterwards. But the beam current always decreases with decreasing energy. In spite of some screening against the spurious electromagnetic fields coming from the environment, particularly the a.c. ones, which is secured by the material of magnetic circuits, some undesired influence is usually observed. This grows strongly at low energies and is proportional to the time of flight through the column, i.e., to E-1/2. The situation is most critical in the ultrahigh-vacuum (UHV) devices where the chamber walls are traditionally made of nonmagnetic materials. Any narrow directed beams of charged particles suffer from mutual interaction of those particles via Coulomb forces. Particularly in crossovers, the mutual repulsion intensifies so that the size of these crossovers becomes larger than that given by geometrical optics. The consequences of the inner interaction are strongly dependent on the beam current, and for low currents and Gaussian beam profile the crossover broadening is proportional to E -3/2 (Spehr, 1985). In connection with the previous point we should also mention that another consequence of the electron-electron interaction within the beam, and again mainly in crossovers, is broadening of the energy spread (so-called Boersch effect). Here again the situation depends on the beam current and also on the crossover shape and dimensions; for stigmatic focusing the mean quadratic broadening AE is proportional to E 1/4 (Rose and Spehr, 1980) so that figures are even slightly more favorable at low energies. The conventional detector of secondary electrons of the EverhartThornley (ET) type (Everhart and Thornley, 1960) relies upon extraction of SE by means of the front-grid bias to about 300 to 500 V and subsequent acceleration of them with the scintillator potential of
SCANNING LEEM
319
about 10 kV. These electrostatic fields, oriented laterally to the optic axis, might be found damaging to the primary beam geometry in the low-energy range. Thus, novel approaches to the detection strategy are needed. With decreasing electron energy and reduction of the active depth of signal generation, the surface cleanliness becomes more important. At energies near to the minimum of IMFP the penetration depth of PE becomes comparable with the thickness of contamination layers, both that of the graphitic carbon from cracked hydrocarbon molecules and that of oxide or other products of the surface reactivity. From this point of view, the vacuum conditions within the specimen chamber become more important, as in the case of electron spectroscopies. However, in the very-low-energy range the IMFP again extends and normal vacuum demands are restored. It is obvious from this list of issues that major obstacles arise from physical principles and can only be avoided by keeping the primary electron beam at high energy for as long as possible and decelerating it only shortly before its impact on the specimen. This approach has already been applied in various modifications that will be outlined here and completed with some new data and experience of the authors.
III. INTERACTION OF SLOW ELECTRONS WITH SOLIDS
The physics of electron scattering and diffusion in solids is described in many original papers and also good textbooks. Precise and sufficiently detailed analysis of the problem for nonspecialists can be found in the book of Reimer (1998) and a condensed review of the scattering phenomena suffered by very slow electrons has been published by Bauer (1994). In this chapter we summarize the main approaches only briefly and depict basic differences inherent to low- and very-low-energy ranges. Elastic scattering on atom nuclei and inelastic scattering connected with excitation of electrons belonging to the target are fundamental processes determining the range of incident electrons, in-depth distribution of the ionization processes, and consequently also emission of the secondary and backscattered electrons. In order to characterize the individual scattering processes, usually the quantity known as the differential cross-section d~/d~2 is used, which shows the relation between the distance of the original electron trajectory from the scatterer and the angle of its deflection 0, and represents the probability that an electron approaching the target will be scattered into a solid angle d~2.
320
MULLEROVA AND FRANK
Integrating over f2 we get the total cross-section cr. Multiple scattering is described via statistical quantities, first of all by the mean free path between collisions. Multiple elastic scattering causes broadening of the incident beam up to possible backscattering while multiple inelastic scattering causes gradual loss of the electron energy along its trajectory. For us, the most important inelastic process is release of a secondary electron.
A. Elastic Scattering 1. Scattering on Nuclei
Scattering of incident electrons on nuclei of the specimen atoms is considered elastic when the mass of the nucleus is regarded as so large with respect to the mass of the electron that after interaction the nucleus remains in rest. This simplifying assumption neglects generation of phonons, which becomes apparent particularly at the lowest electron energies where other losses already vanish. Nevertheless, we will mention this type of scattering among the inelastic types. In the frame of classical mechanics, we can solve the Newton equation containing the attractive Coulomb force between a positively charged nucleus and the negative charge of an electron. The result of the classical calculation of the differential cross-section, first published by Rutherford in 1911, is (for electron energies negligible with respect to the rest energy E 0 = me 2 = 511 keV) given by dcrez
e4 Z 2
1
dr2 = 16(4rce0)2E2 sin4(0/2)
(1)
where e and m are the electron charge and mass, respectively, e0 is the permittivity of vacuum, and Z is the atomic number of the nucleus. This relation is acceptable for electrons above 100 keV but at low energies it represents a bad approximation. It diverges at 0 = 0 because the small scattering angles arise for electrons flying far from the nucleus where in fact its potential is screened by electrons of the atom. At large scattering angles the approximation also fails owing to neglect of relativistic effects (Reimer, 1998). The screening effects can be described solely by quantum mechanics by determining the scattering amplitude f(O) of a spherical wave scattered on the atom and superposing it on the incident plane wave. The differential cross-section is then generally expressed as daez/dfa = If(O)l2.
(2)
SCANNING LEEM
321
The scattering amplitude for the screened Coulomb potential can be found by solving the Schr6dinger equation for ground states of the atom electrons. A good approximation is the exponential screening with the screening radius equal to R s - a i _ i Z -1/3, where a/4=0.0569 nm is the Bohr radius; this gives, after substitution into Equation (2), the so-called screened Rutherford cross-section dote1
e4 Z 2
1
dr2 = 16(4~e0)ZE 2 [sin2(0/2) + sin2(00/2)] 2
(3)
with 00 ----X/2TcRs (Reimer, 1998). This cross-section already produces finite values for small 0 and can be further improved by taking into account the full series of exponential potentials instead of only one, by incorporating potentials from neighboring atoms (e.g., via so-called muffin-tin model), by modification of the scattering potential by correlation and exchange phenomena between incident and target electrons, etc., and/or decomposition into partial waves can be used. The exact cross-sections, so-called Mott cross-sections (Mott and Massey, 1965), for elastic large-angle scattering may be obtained for the screened Coulomb potential when the relativistic Schr6dinger or PauliDirac equation is used. The result is then in the form of a superposition of terms belonging to both spin directions with respect to the direction of propagation but no analytical expression for da/df2 can be written. For an unpolarized electron beam, the Mott cross-section remains axially symmetric and in the general Equation (2) two formally identical members are summed on the right-hand side. These can be then developed into a series of Legendre functions (e.g., Ding and Shimizu, 1996). In addition to modified values at large scattering angles, the Mott cross-sections exhibit one property not met before, namely nonmonotonic angular dependence as shown in Figure 3. Obviously, this behavior emerges in the lowenergy range for large Z while for small Z it is not present until near the very-low-energy range. Data regarding the Mott cross-sections for chemical elements at low and even very low energies can be taken from numerous sources (see, e.g., Reimer and L6dding, 1984; Czyzewski et al., 1990; Werner, 1992). The role of the electron spin in scattering was examined by Kirschner (1984). When decreasing the energy of incident electrons toward the verylow-energy range, the Mott cross-sections, expressing a relativistic freeelectron scattering incorporating partial waves, overestimate the scattering rate and bring unrealistic short elastic mean free path (EMFP) in tenths of nm only. It was suggested (Fitting et al., 2001) that they should be
322
MOLLEROVA AND FRANK
10 "is
~;x" k ~
AI
Au
x
10 "17
V i \ kLg..~,0kev 10 "16
"" "
~I,,
~4[,...._.7.0
;.o2:7 10 "21 0
.
.30 .
.
60 . . . 90. . 120 scattering angle, 0
150 '
v 10"o - .
-180 '
keY
.
3'0.
.
.~o . =- " 9'0 ~2o scattering angle, 0
~,o
~8o
FIGURE3. Differential cross-sections for elastic scattering of electrons at various energies, calculated by decomposition into partial waves. (Reprinted with permission from Ichimura, 1980.)
replaced here with factors inherent to quasi-elastic scattering on acoustic phonons; this mechanism works down to the thermalization threshold of electrons at mean energy 3KT/2, i.e., a few tens of meV, and preserves E M F P in the nm range. Then the scattered electrons are considered as quasifree Bloch electrons within a dispersion relation of the conduction band of the target. Acoustic phonons have energies of a few meV only, but scattering on them is nearly isotropic so that they effectively influence any oriented stream of electrons and, for example, lower the electric conductivity. While the total elastic cross-section (Tel characterizes a single scattering event, the multiple scattering is described by the E M F P
)~el
--
1/Naet
(4)
where N is the number of atoms per unit volume. As Figure 4 shows, this quantity also exhibits nonmonotonic behavior starting from the low-energy range. We can conclude that, for slow electrons, anisotropy appears already in scattering on single atoms and resulting features then combine with a directional segregation owing to interference of partial waves from a lattice of scatterers. Further, the path length between the scattering phenomena generally shortens down to the lowest energies but in the very-low-energy range this dependence is far from being monotonic.
SCANNING ~
I
O
Z
~ /',,"_ .....
IZ
_ i0o
to'
-
J
---:--::
/,,"
..~,
....
i II ,.-.. . . . . Wt.; ," / ' .,,"........,.">;~,." z;.r I0 I= / .." ' :. . ~ / : . . ' " , , . . . . ~ . .,,;~"
/
9;,"~-'~;,5;I..:.~:-",,,.--.~.I",,;,c.,-
........
.
--:.;-:-..::::;::,-
I--~ ~ f-f.-
,,
o
.. . . " i B
I
C ..-...-...-..-
,..'.-'",.-;,""
Cu I-~~ .,:... p).<
323
102
.......... Ge
["
LEEM
......
]" i #~ ; ,,~...... 2 ,~.~"x_;: I,, 9 i.~.-~" ! 11111
io'
to'
I01
ENERGY (eV) FIGURE 4. Calculated energy dependence of elastic m e a n electrons. (Reprinted with permission from Ding, 1990.)
I
I01
!
,, iii!
I
! 1t
I1
10 3
ENERGY leVI free paths
(EMFP)
for
2. Reflection on Energy Gaps Even above the vacuum level, the energy band structure exists and the energy states E(k) are separated by forbidden gaps, particularly where the kvector touches the boundary of the Brillouin zone. If the incident electron hits the gap, it does not enter allowed states and should be reflected. Nevertheless, total reflection is not obtained because the electron can pass an inelastic collision and lose energy or it changes its wave-vector owing to scattering on a phonon or some crystal imperfection--in both cases a shift to the allowed states can occur. In the range of units of eV elastic reflection is strongly enhanced. Electron microscopists have never had any reason to take this phenomenon into account, as its appearance requires the electron impact to be far below the energy range available in the SEM. But those using the VLEED (very-low-energy electron diffraction) method know the energy band structure region existing on the intensity vs. energy (I-V) curve for the specularly reflected (00) spot below the threshold where the first nonspecular diffracted beam appears (Jaklevic and Davis, 1982). It is important to note that the incident electron wave has to couple to the energy states into which it is to penetrate. This means those Bloch states inside the specimen, the surface-parallel wave-vector component of which is equal to KII-4-g, where KII is the vector component of the incident electron and g is any surface reciprocal-lattice vector (Strocov and Starnberg, 1995); in other words, those Bloch states that have dominant Fourier components resembling the incident wave (the coupling bands). The local extremes on the energy dependence of reflectivity R(E) are first of all connected with critical points of the energy bands E(k) at which OE/Ok_Lexhibits sharp changes or is equal to zero at the band-gap edges. When mapping those
324
MOLLEROVA AND FRANK
critical points upon variation of K,, complete bands in the symmetry planes of the Brillouin zone can be compiled (see Strocov et al., 1996). A further crucial condition is low absorption of electrons, which is met below landing energies of 25 to 30 eV. Simulations show that any local R(E) features are washed out at even moderate absorption (appearing for the imaginary part of the crystal potential exceeding 1 eV) and that the model fits better the experimental data when the nonisotropic situation is considered with absorption reduced in directions along the surface (Barto~ et al., 1996). In addition to extremes of R(E) revealing the critical points at the coupling bands, oscillations might also appear as minor features. These are connected with surface resonances caused by interference between the specular beam and a nearly emerged nonspecular diffracted beam moving parallel to the surface, and can be used for mapping the surface potential barrier (Jaklevic and Davis, 1982). Figure 5 demonstrates the reflection anisotropy connected with its k vector dependence, which enables one to get contrast between different crystal orientations at suitable energies. Mapping of the local variations in the density of states at the energy of the electron impact, for example those connected with the local doping of semiconductor structures, is also potentially available. B. Inelastic Scattering The term inelastic scattering is usually used to describe an interaction between the incident electron and the atomic electrons in the target. More generally, this should include all phenomena at which the impinging electron changes its energy. 1. Scattering on Electrons The main mechanisms of interaction between electrons include: 9 9 9 9
quasifree electron-electron collisions (i.e., a Compton-like scattering), excitation of electrons within partially occupied energy bands, excitation of interband transitions, excitation of plasmons, i.e., energy quanta connected with the charge density waves of valence or conduction electrons, and 9 ionization of inner shells of the atoms.
These mechanisms exhibit not only various cross-sections, but also represent very different amounts of energy interchanged between colliding particles. Although inelastic scattering is often assumed to cause only energy decrease
325
SCANNING LEEM
1.0
. . . .
II
I
'
i"
il
0.0 0.6 I,,i,J I:K
O.t,,
0.2 ei | n
"....:
0
!
,.
,1
1
a
5
10 E(eV)
15
20
FIGURE 5. Reflection coefficient R(E) of the W(ll0) and W(100) surfaces for slow electrons. (Reprinted with permission from Bauer, 1994.)
but not trajectory deflection, some collisions can be associated with large scattering angles (like the Compton scattering). In spite of this, the relevant differential cross-section is often considered in the energy scale instead of in the angular one, namely as d a / d W, where W is the transferred energy. Energies transferred at ionization range from a few eV up to nearly 100 keV depending of the atomic number and electron shell involved. Excitation of plasmons and electron transitions cause energy losses not exceeding tens of eV but the loss due to the electron-electron collision can be up to 50% of the initial energy. If we neglect any binding forces acting upon the target electron at rest and consider the incident electron approaching with energy E, we can use classical mechanics to get the differential cross-section (Reimer, 1998) dain
dW
~e 4
1
(4~e0) 2 E W 2"
(5)
This relation is derived upon the assumption that the target electron stays at rest during the collision and only acquires momentum--this is not the case for slow electrons and hence for E ~ 0 (and also for central collisions) this cross-section diverges. But Equation (5) indicates that this type of scattering is more common at low energies, that small energy losses are
326
MOLLEROVA AND F R A N K
more probable, and, because the same approximation gives the scattering angle 0 as sin20 = W / E ,
(6)
small scattering angles are also more probable. If this simplified approach is upgraded, correcting terms due to indistinguishability of electrons and due to their spin are added to 1/W 2. These are of the same dimension (energy) -2 and combine E, W, and E0. Thus, the added terms also grow at low energies but for W<< E these corrected relations converge to Equation (5). An equation derived by Gryzinski (1965), which takes into account the binding of electrons in atoms, also converges to Equation (5) for low binding energies. In fact, the "continuum" of losses owing to scattering on quasifree electrons appears in the EELS (electron energy loss spectroscopy) spectra only in the range of hundreds of meV (Reimer, 1995). The inner shell ionization can be solved in the same way as the problem of screening of the nuclear potential, i.e., by using the Schr6dinger equation for the nucleus, one atomic electron, and one incident electron, which leads to Equation (3). Now, excited states of the target electron are incorporated too and the final result, the total cross-section, e.g., for ionization of the K shell, is (Reimer, 1998) roe4 O'K -- (4~:e0)2
z x b x In u E2
(7)
u
where z/r is the number of electrons in the shell (z/r= 2), b/r is a constant factor (b/r = 0.35), E/r is the ionization energy of the shell, and u = E/E/r is the overvoltage. A maximum of a/r appears at u ,~ 3 for all atomic numbers and at lower energies a/r steeply falls. This means that throughout the lowenergy range the electron impact ionization is possible for every atom but in the very-low-energy range this type of scattering does not take place. The differential cross-section from the same calculation is
[(
dain _ e4Z as2 - (4rce0)ZE2 1 -
1 1 + (02 + 02)/02
)21
1 (02 + 62) 2
(8)
where the characteristic angle is OF_,--J/4E with J being the mean ionization potential of the atom (J [eV] ~ 10Z) and 00 is that from Equation (3). This relation is similar to Equation (3) and we can compare two characteristic features. First, at E = 5 keV the inelastic scattering is still confined to smaller deflection angles (e.g., for Z = 30, 00 is 10 times larger than 0E) but this
SCANNING LEEM
327
difference is less marked at lower energies. Second, the ratio of both differential and total cross-sections for inelastic with respect to elastic scattering is proportional to 1/Z, at least for large scattering angles. Within so-called dielectric theory, considering the solid described by the complex dielectric constant e and employing the analogy between the inelastic scattering of electrons and spatial attenuation of electromagnetic waves being proportional to the imaginary dissipative part of e, the differential cross-section can be written as (e.g., B6ngeler et al., 1993) d2tYin 1 Im[1 ] 1 d W d--------~- Tc2 aH----------~ e(W, 0) 02 + 02
(9)
with OD= W/2E. The analogy is based on modeling groups of electrons, similarly strongly bound within the given energy-band structure, by oscillators defined by their strengths and characteristic frequencies. So the problem is now shifted to determination of the complex dielectric constant e. Similar relations and results as regards the inelastic cross-sections are obtained when using the formalism characterizing the incident electron as a quasiparticle with self-energy, the imaginary part of which describes the quasiparticle lifetime while the real part expresses the shifts in the energy eigenvalues with respect to the noninteracting system. The same holds for the formalism of the electron-jellium correlation potential with the imaginary part governing attenuation of the dielectric response of jellium to the electron impact. Equation (9) used to be written also in variables W and q (the momentum) or q and w (with W = hw/2Tc). An overview of these approaches was published by Nieminen (1988). The energy loss function, written as Im[-1/e(q, co)], can be calculated on the basis of EELS experimental data for q = 0 (the "optical" data) when employing, for example, the quadratic dispersion relation (Kuhr and Fitting, 1999) ~o(q) -
~o(o) + ~
h
q2
.
(10)
Figure 6 shows an example of the measured dielectric loss function for SiO2 (Fitting et al., 2001). This contains peaks inherent in scattering on optical phonons, which will be mentioned in the next section. Calculations of quantities characterizing the inelastic scattering, which employed the dielectric function, were performed by many authors (e.g., Cailler et al., 1981; Powell, 1974, 1984, 1985; Penn, 1987; Egerton, 1986; Ding and Shimizu, 1996).
328
MULLEROV,~tAND FRANK
0
0.01
0.1
1 10 energy loss (eV)
100
1000
FIGURE6. The dielectric loss function for SiO2. (Reprinted with permission from Fitting et al., 2001.)
In Figure 7 we see the calculated energy dependences of ain for two elements, including the main contributions to crin. These curves reflect the general IMFP curve in Figure 2, which we used for the definition of the very-low-energy range (with IMFP, )~i,, defined analogously to Equation (4)). Further data regarding the IMFP behavior at low energies can be found in the work of Ding and Shimizu (1996), Powell (1987), Tanuma et al. (1991a,b), and others. We can notice that, starting from lowest energies, first the electron-electron scattering appears, then the ionization, and finally the plasmon excitation emerges. Let us repeat that the steep drop in crgnbelow about 50 eV is the most important feature here and also the reason for considering the use of this range as a separate mode of SEM. 2. S c a t t e r i n g on A t o m s
In the dielectric loss function in Figure 6, noticeable peaks that appear around 100 meV belong to scattering of electrons on optical phonons. Having formally separated the inelastic phenomena due to scattering on electrons in the previous paragraph, we discuss this mechanism here. The electron-phonon interactions are important mainly in dielectrics and insulators, but also in semiconductors. The forward scattering on longitudinal optical phonons (LO) is strongest. In 1969 Llacer and Garwin calculated (by means of Monte Carlo simulations) the secondary electron transport in alkali halides below 7.5 eV using the time-dependent perturbation of plane waves with the interaction Hamiltonian containing the polarization field caused by relative displacement of ions in the LO vibrational modes. Schreiber and Fitting (2002) discussed these phenomena in detail for SiO2 and included two LO modes with energies
SCANNING
LEEM
CTin[Cm 2]
329
o AI
1 0 "15
1 0 "15 I
1 0 "16
1 0 "16
; I
,i
\
-,~ \
"'... ".. " . \
" . . "-..",,
I..'
"
II 10"1'
1 0 "17
1
10
1 O0
1000 E[eV]
i
i . i Iil .
1
10
. .. . .
100
.
.
'\. .
"'~
"\-,,
1000 E[eV]
FIGURE 7. Calculated total inelastic cross-sections ( ) and their main contributions, namely the electron-electron scattering ( - - . - - . ) , shell ionization (. . . . . . ), and plasmon excitation (. . . . . . ). (Reprinted with permission from Ho et al., 1991.)
of 60 and 150 meV and also scattering phenomena representing both emission and annihilation of phonons. They also presented the scattering rates of collisions, which are much higher for the phonon emission phenomena. At about triple phonon energies, these rates reach their maxima between 1014 and 1015 s -] and toward higher energies they fall approximately as E -]/3. Thus, this scattering mechanism concerns mostly electrons with energy around 1 eV. It seems clear that, even when incorporating the phonon scattering, the enlargement of IMFP in the very-low-energy range (see Figure 2) is preserved at least for conductors and possibly for semiconductors. In Figure 8, comparison is made on the basis of data simulated by the Monte Carlo (MC) program employing the dielectric loss function (Kuhr and Fitting, 1999). Further, Figure 9 details the contributions to IMFP for SiO2, again presenting results of a MC program specialized to the very-low-energy scattering in semiconductors and wide-gap insulators. In addition to the mean free paths, both figures also contain the attenuation lengths characterizing a no-loss escape of electrons. We note that the energy range below 50 eV still has some structure in Figure 9, which could be utilized for the subdivision of this range. Nevertheless, this would be specimen-specific and would not allow any general conclusions to be drawn. In studies of the very-low-energy electron scattering, one more scattering mechanism is mentioned, namely the intervalley scattering (e.g., Schreiber and Fitting, 2002). This consists of collisions with suitable optical phonons, at which, in addition to energy loss corresponding to the phonon energy, additional energy and also momentum is transferred because the final state is in a different band or "valley" within a multiple-band structure. For SiO2, this type of scattering occurs much less frequently than the LO scattering.
330
MULLEROV,~ AND FRANK
i iimmk 10 l i i....... -"! I llllll--__tinel. i
mllmlll
m I'l'/
II!
l *,[ X',',',', I*, ........... ill,
-I
A~
Ii
i lllllll
n ,-,u II llilIHi I lllliil I IIIIIIII
Illl IWll
'"))11 I lllllll I I IIIIlil kr i [Ill !,[11,1, I,,,,,[[, ~'lll
[n~m]
IIImlll
,k ........
j ~ ,. ,
Illlllllll
I!i111111 , SI I I |1111111 . J lllllll
1 llllllll
il',lmm',mm[)~I[ II1111
igll
I!!!!! !
yllt
nel. ~111 ....
![ILLIILI/llL!'l![L!II ,,
l'kl.lllll ,I~I#IIHIII
IIIIIII 9 9
I i lilill/l:,l't iiliil
~
IIIIH
I lillllll I
a~o,.,. ~Itll~'llliiilll ill l lllltlll l"?lliiU
0.1
I,Im IIIIIIII Ir IIIIIIII IIIIIIIII I 'i
" IIIIIII IIIKi'llll J/IIIU]III I I1UUII IIlilV, t i
!
~;~ii:,i < ~,I,
i i ilmml'rl
,,,,,,'" i :, I IIIIIII
II
m,.7,,,,.,2 II ! l llml " !!!!!!!! !11111111 i,~
I l ltlllll 1 ~IIIIIII
nii~l][] IIIIIII ,ll[llli,lll
/II1[111~ IIIIIIII111111111/,7111
......
i iiiiiii
,I , , I,I,I I I U I. . . . . . . . . . .II. O | i l ~
ilUllii IIIIIII
I
l llllll
I
III
I Wl, i l l l l l
]
i
il
i iiii!!!,iiiiill i liillli
I J
I~llilll~
il'Ill~ I IIlillll
ii
I i liliiK k I I K~'fllllk Idlll~dl
~ltlmll
i lU~ a~n., ~ill I IIIUIII !
]iiiii]ii;i'hl1111111 II Llll ]llllil,i',II1111iiiiiii III]! Illllllll ,,,,,,, IIillllll 1
10
100
1000
1
10
100
1000
10
1
100
1000 E [eV]
FIGURE8. Elastic (el.) and inelastic (inel.) mean free paths and attenuation lengths (atten.) for Ag, Si, and SIO2, calculated by means of a MC program incorporating the Mott crosssections and the dielectric loss function. (Reprinted with permission from Fitting et al., 2001.)
numB
mmll
lie m~.n
m
mmm
~m|
-_-~
:i
i
m
m m m
III !111 0.01
.~ 0.1
1 energy
10 E (eV)
100
_ 1000
FIGURE 9. The mean free paths in SiO2 as a function of the electron energy for scattering at optical phonons (LO) and acoustic phonons (ac) and for impact ionization (ii), together with the attenuation length (at) for monoenergetic electrons. (Reprinted with permission from
Schreiber and Fitting, 2002.) For completeness we should also mention here the inelastic scattering of electrons on the screened Coulomb potential of the nucleus, leading to generation of an X-ray photon of the continuous emission (Bremsstrahlung emission). The low probability of radiative scattering on the nucleus can be demonstrated by comparing the ratio of the mean energy loss per unit trajectory Sraa to the analogous quantity for the electron-electron scattering. When using an approximate stopping power Se_ e according
SCANNING LEEM
331
to the Thomson-Whiddington law (see next section), we get the ratio (Feldman and Mayer, 1986)
Sraa4
Z (V) 2 Se-e -- 3r~ 137 c
(11)
which can be simply written as (Z/161) E/Eo so that in the low-energy range it falls to a value of the order of 10-3 or 10-4.
C. Penetration of Electrons The primary beam in SEM strikes the specimen surface at a point, the coordinates of which within the field of view are then used to describe the localization of all information collected during the dwell time of the beam. Nevertheless, the primary electrons penetrate to nonnegligible distances in all directions from the impact point and within this interaction volume they cause scattering phenomena and generate signal species. Thus, the abovedescribed single-scattering mechanisms are important not only for interpretation of the observed properties of emissions but also for tracing the spatial distribution of the information sources. The analysis of the electron penetration goes through the concept of multiple scattering, which can be characterized by statistical quantities only. We have mentioned the mean free paths for individual types of scattering. From Figures 2 and 4 or from Figure 8 it is obvious that, throughout the low-energy range, the ratio of rates for elastic and inelastic scattering is approximately constant and dependent on the mean atomic number of the target. The very-low-energy range is characterized by the onset of a strong dominance of the elastic scattering. When penetrating into the specimen (and, after undergoing some highangle scattering events, also into lateral directions) by a distance dx, the electron encounters N dx atoms (where N = NAp/A is the number of atoms per unit volume, Na is the Avogadro number, p the target density, and A the atomic mass). Thus, the decrease in the stream of unscattered electrons within the trajectory section dz is dI/I=-aNdz, where a is the total crosssection of one atom for a particular scattering mechanism. The unscattered intensity after passing the thickness l is I = I0 exp(-//)~) (with)~ as the mean free path), p=l/)~ is the mean number of collisions in the layer, and Pn =p'e-P/n! is the probability of n collisions for one electron. This simple model can be used only up to about p ~ 25 (see Reimer, 1998), i.e., only for tracing the penetration to distances of the order of 101 nm.
332
MI21LLEROVA A N D F R A N K
In the course of its penetration, the electron beam broadens as regards both its spread of angles and also its cross-section. Within the approximation of small energy losses and small scattering angles, the rootmean-square (RMS) width of the beam increases as l3/2 (Reimer, 1998). Nevertheless, this approximation is not good for low energies and successful modeling of the geometry of electron penetration is possible only by using tools such as MC programs. The multiple inelastic scattering is responsible for the finite length of the electron path within the target. The appropriate statistical quantity for the examination of this process is the stopping power S = dEm/dx (with dEm for the mean energy loss), corresponding to the continuous slowing-down approximation. This approach, which neglects discreteness of the collisions, does not allow study of the emission of elastically backscattered electrons (eBSE) but is useful for MC programs simulating the SEM image signals. When taking into consideration the e-e interactions only, the so-called Bethe formula, usually written as (Reimer, 1998)
2Tce4pZ NA ln(1 1 6 6 j )
(12)
S - (4~e0)ZE A represents the first approximation. For composite targets, the individual stopping powers have to be accumulated so that the relation for S contains a sum of terms like cm(zi/Ai)ln(bE/Ji), where C m are the mass fractions. This sum is often replaced by some energy-independent factor and the resulting expression is then called the Thomson-Whiddington law. Another practically convenient form of the stopping power relation for elemental targets is (Joy and Luo, 1989) S-
IoZ
-7850 ~
Zi
E
Z . ~- In ~//
[eV/nm]
(13)
l
where p is in g cm -3, Z i is the occupancy of the level i, and El. its binding energy. Equation (13) is claimed to work down to the binding energy of the outermost occupied level. While the differential cross-sections for the main scattering mechanisms are all proportional to E -z, the stopping power according to Equations (12) and (13) increases only as E -1. The validity of approximation (12) is restricted to high energies, notably in the dependence on the ratio E/J, so that for light elements it is acceptable down to about 1 keV. For lower energies, the correction J--+ J' = J/(1 + k J/E) with k TM 0.8 is possible. Below E/J 6.3 the energy dependence of S used to be replaced by S (x E -~ (Rao-Sahib and Wittry, 1974) but some authors assert that this parabolic =
SCANNING LEEM
333
relation overestimates the energy loss of slow electrons (see Ding and Shimizu, 1996). In the very-low-energy range, the stopping power seems to behave according to the statistical theory of Tung et al. (1979), in which electrons in the target are considered to form a homogeneous electron gas. Then S cxE s/2 for all targets (Tung et al., 1979; Nieminen, 1988), which corresponds to the sharp fall obvious in Figure 7. A theoretical model exists also for the most probable electron energy after passing a layer of the target, together with the distribution around this mean value. For SEM applications, the energy distribution of the backscattered electrons, which is mentioned below, is relevant. From the practical point of view, we need to know to what depth the primary electrons penetrate and what is the escape depth of the signal species. Various quantities have been defined to measure these distances and one of them is the attenuation length shown in Figures 8 and 9. The most useful is the electron range R, which can be defined in several different ways according to the method of measurement (see Reimer, 1998). Determination of the electron range is possible via measurement of the number of electrons T(x) passing a foil of a given material with some known thickness x. Because R depends also on energy E, it is convenient to use one foil thickness and to vary the energy. It is also advantageous to use an extrapolated value Rx (obtained by extrapolating the linear part of T(x) toward T = 0) instead of measuring down to really negligible transmission in order to get s o m e Rmax. Most of the experimental data obey a simple law R=aE n
(14)
with a around 10 and n decreasing from 5/3 at high energies to about 4/3 at low energies (B6ngeler et al., 1993). This relation seems to be valid down to about 1 keV and only few data exist below this energy. Salehi and Flinn (1981) verified the power law (14) for the penetration depth using two different amorphous glasses within the energy range 100 to 5000 eV and found n as 1.4 and 1.5 with the larger value for higher mean atomic number. The theoretical limit for the electron range can be obtained by integrating the stopping power S up to the particle "stop," which gives some Rs. Experimental data will provide lower values. According to Reimer (1998), for light elements with Z below about 20 we get Rmax ~ Rs and Rx ~=0.75Rs, while for high Z above 50, Rmax < Rs and Rx ~- 0.4Rs. Below 1 keV the electron range Rs exhibits a smaller slope of descent with decreasing energy than the data obtained by measurement of T(x) (Joy and Joy, 1996). Also the MC simulated electron range, as demonstrated by Kuhr and Fitting (1999) for Si and Au, has the slope decreasing below 1 keV
334
MOLLEROVA AND FRANK
toward a nearly energy-independent behavior at 100 eV, with values of 10 nm for Si and 6 nm for Au. One further parameter of the electron beam penetration is the depth distribution of the energy dissipation. The interaction volumes of the beam are roughly the same size for all specimens when distances are measured in the mass thickness px. Nevertheless, as the MC simulations show, for light elements the majority of scattering events is concentrated in the central level of the volume and somewhat below it while for heavy elements more scattering takes place above the central level.
D. Heating and Damage of the Specimen In introductions to papers dealing with low-energy microscopy, especially those concerning the instrumentation, we often meet formulations stating that the low energies are advantageous because of reduction in the specimen radiation damage. However, this opinion is wrong in most instances, at least within the low-energy range usually meant in the statements cited. Although the slow electrons really deliver less energy per impact, their interaction volume shrinks strongly and the spatial density of energy dissipation even increases. If the primary beam spot is considered stationary and its interaction volume hemispherical of a radius R/2, the temperature increase in the illuminated point amounts to (Reimer, 1998) AT
-
3dUI 2~cR
~
(15)
where U and I are the accelerating voltage and beam current, respectively, d is the portion of the incoming power that is dissipated into the specimen, and c [Js-lm-lK -1] is the thermal conductivity of the target. Obviously, the heating is proportional to E/R and because of Equation (14) AT increases at low energies. This heating is naturally higher for any noncompact material; e.g., for fibers it increases roughly in the ratio of their length to diameter (Reimer, 1998), and cannot be significantly suppressed by surface metalizing because of insufficient cross-section of the metal layer. When considering the electron probe scanning an island of area SA of a layer of thickness l >_R/2 from a low thermal conductivity (e.g., organic) material deposited onto a metal surface, we can derive the simple relation for its heating
A T -- djU ( l - R/4) c
(16)
SCANNING LEEM
335
with the illumination current density j = I/SA. Now we get AT decreasing at low energies but when SA denotes the size of the field of view on a larger area of this organic material, the lateral heat escape can reverse again the energy dependence of the heating, according to the relation between SA and R 2. In the low-energy range, the energies of emitted SE and BSE are still so different that in spite of the SE yield 8 being higher than that of BSE, r/, the energy output mediated by SE can be neglected. Thus, d ~ 1-rl and it remains nearly constant over the low-energy range. Further, because of 8 e~ E -~ (Drescher et al., 1970) at energies sufficiently above the maximum of 8, i.e., above, say, 2 keV (see the next section), we can operate with the primary current decreasing in the same ratio with the decreasing energy. Taking this into account, we find (even in Equation (15)) that the specimen heating slowly decreases at low energies down to about 2 keV where the increase starts again. The temperature distribution around the moving electron probe was studied by Kohl et al. (1981). For common materials, particularly metals, semiconductors, and even insulators with sufficient thermal conductivity, the temperature increase remains far below 1 K. Nevertheless, some materials such as foams and gels have very low thermal conductivity and their heating might be critical. These specimens were studied by, for example, Brown and Swift (1974), Berry (1988) and Price and McCarthy (1988). Mostly low-energy modes are recommended for sensitive specimens. The direct radiation damage of the specimen material consists first of all in breaking the chemical bonds, decomposition of molecules, and possibly release of gaseous components. Because it is generally ionization phenomena that are in question here, the energy dependence can be assessed according to the stopping power S. According to Equation (12), S cxln(E/J)/E, i.e., approximately S cx E -~ This is an even steeper slope than that of E -1/3, which results from the simplest assumption about the beam energy tlE/e (with t being time) distributed homogeneously into the depth measured by R cx E 4/3. Hence the spatial density of the radiation damage events increases throughout the low-energy range. For organic molecules the radiation damage mechanisms are diverse and it is not possible to survey them here. Let us briefly mention semiconductors. Incident electrons generate, for example in silicon, electron-hole pairs and holes can be trapped in the SiO2 layer where they have much lower mobility than electrons. Hence the density of surface states on the SiO2-Si interface increases, which in turn increases the rate of surface recombinations and the generated space charge might even cause layer inversion. For example, in MOS (metal-oxide-semiconductor) structures, the electron bombardment can induce changes in the threshold
336
MULLEROVA AND FRANK
voltage, gain, and dark current, i.e., in all the important parameters of the device. Some of these effects disappear only after long heating to temperatures above 250~ Nevertheless, significant suppression of these influences has been proved for electron energies below 1 keV, which are also used in IC (integrated circuit) testers. A special kind of radiation damage consists in breaking the carbon bonds to oxygen, hydrogen, and other atoms in hydrocarbon molecules. Owing to their high sticking coefficients, these molecules are always present on the inner walls of vacuum vessels including the specimen surface, unless this has been prepared or cleaned in situ. The carbon atoms then close double bonds and create a "polymerized" graphitic layer, the thickness of which progressively grows owing to easy diffusion of additional hydrocarbon molecules from the nonilluminated neighborhood of the field of view. Consequently, dark rectangles with darker frames indicate the areas of previous observation; these effects were studied by, for example, Fourie (1976, 1979, 1981) and Reimer and Wfichter (1978). At low current densities, the contamination thickness is proportional to dissipated energy, i.e., to the stopping power (which increases down to the boundary of the very-low-energy range). When all the molecules that have diffused into the illuminated area within a time interval are cracked in that time, the contamination rate saturates and then the contaminant accumulation becomes linear in time. As indicated above, the carbon contamination rate increases with decreasing E; according to experience, the situation around 100 to 200 eV is the most critical. Let us underline that, within a certain energy range of a few hundreds of eV, this phenomenon is the main obstacle against routine taking of micrographs (see, e.g., Figure 65). Fortunately, from the beginning of the very-low-energy range, this trend is reversed, elastic phenomena start to dominate, and the radiation damage disappears.
E. Specimen Charging
As already mentioned above, one important reason for using low energies in SEM is to gain an advantage in the perpetual fight of SEM microscopists against specimen charging (see, e.g., Pfefferkorn et al., 1972; Welter and McKee, 1972; Morin et al., 1976). In the next section we will see in more detail that in general the amount of charge emitted from the specimen differs significantly from the incoming charge. The difference is dissipated in the target and when this has a low conductivity, the absorbed current is not carried away from the illuminated area efficiently enough and significant charge density gradients arise. Furthermore, except for glasses and other
SCANNING L E E M
337
(5"m
,,,~e {.r G~~']
l
j
i
I ~ I
I I
I I
I I II eUs>O i r 1 I I
I l i I
I I leUs
I
|
I
I
....
Ecl
-'~,,
_a_~us'
E
l
I I
E Ec2 E
II,
I
E
Ep
FIGURE 10. Typical energy dependence of the total electron emission cr for specimen tilt angles 4)s > 4)2 > 4)] indicating the development of charging processes (see text for details).
homogeneous materials, the nonconductors and particularly specimens from the area of the life sciences are as a rule of a heterogeneous and anisotropic nature. Thus, the specimen charging is usually also inhomogeneous with the result that electric fields that vary strongly both in space and time are created above the surface. These fields destroy the micrograph geometry by deflecting and defocusing the primary beam, and also affect the brightness distribution by influencing the signal electron trajectories toward the detector. Qualitatively the issue can be comprehended from Figure 10. For every specimen, the total electron yield, a = 6 + 7, exhibits a maximum, which for the great majority of elements and compounds and for all nonconductors exceeds the value 1.0. When progressing from the conventional SEM energies around 15 keV downwards, the a(E) curve rises and crosses the unit level at the critical energy Ec2. This is the optimum energy for no charging and we will discuss ways of employing it for practical microscopy in Section VIII. Further, a(E) reaches its maximum at some Em' that more or less coincides with the maximum of the SE emission at Em (see the next section) and then descends, crosses again the unit level at Ecl and enters the range where no general curve can be drawn owing to very diverse behavior of the BSE emission. Finally, a(E)--+ 1 when approaching the mirror microscopy range at and below the zero energy impact. The differences in curves labeled with angles (~i express the angular dependence of the emission, which here means the influence of the specimen tilt and also of local inclinations corresponding to the surface relief.
338
MULLEROV~i AND FRANK
Suppose now the primary beam incident at energy E~>Ec2 o n a poorly conducting surface that exhibits a finite leakage resistance Ra between the illuminated point and ground; this is a measure of the ability of the specimen to carry the incoming charge away. We can characterize it by a straight line of slope ( e R J p ) -1 with /t, as the specimen current, which corresponds to a positive surface potential formed on Re. The potential drop across RG partially compensates the negative potential of the accumulated surface charge. The residual local potential decelerates the incoming beam so that its landing energy decreases causing a(E) to increase. This iteration continues until an equilibrium is reached at the point A for the final landing energy E where the incident and leakage currents are equal, leaving some net surface potential Us
S C A N N I N G LEEM
339
some negative charge again. The above-surface field is then dependent on the total charge distribution. Furthermore, the a ( E ) curve cannot be understood as a static property of the specimen since it exhibits a dynamical behavior, the specimen emission yields being affected by the penetrating charged species. We now look at the dynamics of the charging process based on our phenomenological model--these data will be needed for one important SLEEM application described below. F r o m the a ( E ) curve in Figure 10, we easily deduce E- E l a(E) - 1 =- ~ . (17) eRa Ip
Let us assume for simplicity that the charging process is characterized by only one time constant rc so that the accumulated charge develops as Q = Q m a x [ 1 - e x p ( - t / r c ) ] . This time constant will now be determined:
Qmax (18)
rc = (dQ/dt)t=o .
We consider the charged field of view to be a thin circular disc of diameter a and charge density q, situated in a medium of permittivity e. From the Coulomb law and the principle of superposition, we get the disc potential as Us = qa/2e. Figure 10 gives e Us = E - E', so that Qmax ~ qa 2 = 2 e a U s =
2Ea 8
(E - E').
(19)
At t = 0 the dissipated part of the beam current is [or ( E ' ) - 1] I p = d Q ( O ) / d t (< 0 for negative charging). In this equality, we substitute for a(E') the first two terms of the Taylor expansion around E and then substitute for a ( E ) from Equation (17). Finally we obtain
I]
{1
dQ
~ ( E - E') ~ - / t ,
~
.
(20)
t--0
The behavior of a ( E ) for energies above the critical energy can be estimated, according to the relations 17~ const and 6 cx E -~ (Reimer et al., 1992), as a ( E ) ~ - r l + ( 1 - o ) ( E / E c 2 ) - ~ which enables us to take the derivative in Equation (20). Substituting now from Equations (19) and (20) into Equation (18), we find for large RG the final result eaEc2
rc "~ 2.5 eli,(1 - r/)"
(21)
340
MULLEROVA AND FRANK
In order to get some quantitative figure, let us use the values rl=0.2, e r = 4 , Ec2 = 2000 eV, I e = 1 nA as an example. Then the time constant rc varies between 200 gs and 20 ms as the size of the field of view changes from 1 to 100 gm. Practical experience confirms that some charging is nearly instantaneous and might correspond to this range of rc but afterwards further changes in the image are usually seen for seconds or even longer. We stress that the above calculation differs from the approach often met in the literature (see, e.g., Shaffner and Van Veld, 1971; Welter and McKee, 1972; Cazaux, 1986), which considers the charging dynamics to be identical with the charging of a plate capacitor situated between the specimen surface and a metallic holder; then r c - p e . At high resistivity p, this time constant can be very long, e.g., about 3300 s for SiO2. Nevertheless, we recall that we aimed at getting a time constant for the progress in image destruction effects caused by the above-surface field, but the capacitor field is entirely closed between its plates and hence restricted to inside the specimen. A weak point of our approach is that the specimen current is considered to be of an ohmic nature, which might not always be realistic (see Cazaux et al., 1991). The crucial quantity in the above considerations is the critical energy Ec2. This quantity can be easily measured on conductors (via the absorbed current) but the opposite holds for the nonconductors that are of interest here; Reimer et al. (1992) summarized possible methods for this case. While in Figure 1 we have the values of Ec2 for some conductors, Joy (1989) published values for a choice of technologically important inorganic insulators between 550 and 3000 eV and for a selection of polymers, he found Ec2 from 0.4 to 1.8 keV. The 4~ dependence of Ec2, governing the scatter of these properties at rough specimens, can be estimated as Ec2(~b)= E c 2 ( 0 ) sec 2 ~b (e.g., Joy, 1989). This relation suggests that Ecz(60~ but detailed studies showed a less steep angular dependence and this ratio was found to be only around 2 and even smaller for insulators (Reimer et al., 1992). In particular, the angular dependence of Ec2 should weaken in the low-energy range together with the same trend regarding 3.
F. Tools for Simulation of Electron Scattering Phenomena connected with electron scattering inside the target, particularly in the case of multiple scattering met in SEM, are too complex for it to be possible to solve the "direct task," i.e., to reconstruct
SCANNING LEEM
341
the specimen from the SEM image or an image series, as can be done in certain circumstances in the TEM. Thus, efforts were oriented toward simulating the image of a fictitious specimen described by its scattering cross-sections. Two main approaches can be found in the literature: the transport equation approach and the Monte Carlo procedure. The transport equation is the equation for the phase-space density of electrons, n(r, ~, t), dependent on the position vector r, velocity vector v, and time t. All scattering phenomena that influence local values of n(r, v, t), including the generation of the incident beam, can be expressed by integrals containing the corresponding probabilities for movement within phase space (e.g., a (v--+ ~') for both inelastic and elastic scattering, differing by whether Iv[ = [u'l or not) and taken over the rest of the phase space. If a stationary case is considered, the terms increasing and decreasing the local density n compensate mutually, composing some integral equation for n(r, ~). In order to render the equation solvable, some simplifying assumptions are usually made, such as restriction to semi-infinite, amorphous, and in-depth homogeneous specimens with ideally flat surfaces, to multiple scattering corresponding to the Poisson stochastic process, the inelastic scattering being described by the mean free path, etc.; these assumptions enable one to use the Boltzmann-type classical transport equation (see, e.g., Werner, 1996). The simplest solutions then assume that the scattering is restricted to small angles. Program packages utilizing the MC algorithm also rely on the simplifying assumptions mentioned above, except those regarding the homogeneity, semi-infinity, and flatness of the specimen. Otherwise, similar information about the specimen is needed--the differential elastic and inelastic cross-sections or their equivalents, the differential inverse mean free paths. Let us briefly summarize the MC procedure for tracing the scattering of one electron (see, e.g., Ding and Shimizu, 1996). The basic concept is the normalized accumulation function A(x) for some probability distribution function P(x) of a physical phenomenon with one parameter x:
A (x) --
fxx P(x') dx' / l xmaxP(x') dx'. rain '/Xmin
(22)
Obviously A(x) E (0,1) and when uniformly distributed random numbers Tr are taken within this interval and x is calculated from A(x)= R., then after many attempts the assembly of x values obeys P(x). The second basic concept is the rule for deciding which member of a set of n possible phenomena will take place when one must definitely occur. The rule is that
342
MULLEROVA AND FRANK
the ith phenomenon occurs if
n
i
j=l
j=l
s (23)
j=l
j=l
where pj is the probability of the flh alternative. Again, after many attempts the total occurrence of a particular phenomenon corresponds to its probability. Now we can apply Equation (22) to the free path s of the electron provided the scattering probability distribution is that of the Poisson process, i.e., P(S)=(1/)vT)exp(--S/)VT) with 1/)Vr= 1/)Vel+ 1/)~in a s the total inverse mean free path; we simply get s =--)VT lnTr Having determined the free-path section, we use another random number to decide what collision takes place by means of Equation (23) so that Pl = )Vel and P2 = )vin. When simulating the scattering in a compound of m different atoms, the elastic scattering phenomenon can be ascribed to the flh atom according to a j Equation (23) again, now with pj - Cj/)~et, C~ as the atomic fraction. The same procedure can be followed for the inelastic collisions only in alloy-like compounds where the scattering cross-sections can be summed. Otherwise, the compound-specific data for 1/)vin should be acquired. The scattering angle due to an elastic collision is also calculated from Equation (22) with A(x)= 7~, provided P(x) is replaced by dael/dS2; the scattering angle and energy loss for an inelastic event can likewise be found by using d2)~/~1/dr2 d W and dZX/nl/dW, respectively, as the probability P(x). When simulating sophisticated processes such as the formation of an angular resolved energy spectrum of electrons with characteristic energies, in which case only very few of the incident electrons create the relevant signal species, simulation of reversed trajectories can also be used (Gries and Werner, 1990), starting at the detector and finishing at the first inelastic collision. Ding and Shimizu (1996) presented MC modeling of SE generation including cascading processes, which produced energy spectra of SE + BSE emission that fitted the experimental data very well. A detailed study of SE emission from SiO2 by MC simulations was performed by Schreiber and Fitting (2002). These data directly relate to the SEM application. Obviously, both transport function and MC algorithms can be applied on various levels of the physical model, depending of what data for the mean free paths are utilized. For the inelastic scattering, more recent works use the dielectric functions, usually compiled from measured optical data and some dispersion relation, and sometimes a combination of discrete events and continuous slowing down contribution is used or even no discrete events
343
SCANNING LEEM
are considered. For the elastic scattering, all the choices from classical Rutherford cross-sections up to the Mott ones can be found, including the scattering on phonons, as described in previous sections of this chapter. Generally the MC algorithm is capable of working down to very low energies, provided it is completed with adequate scattering data, and only coherent scattering phenomena and effects connected with the energy band structure are excluded. When in the very-low-energy range the scattered electrons are taken as the Bloch electrons within the energy band structure of the target, the electron trajectory, needed for the MC procedure, has to be extracted from E(k), tensor of the reciprocal effective mass ]lm-lll, etc. Then the electron movement in an electric field F is first considered in the reciprocal space as dk/dt=(2ne/h)F, and transition into the real space is made via the real electron velocity (Schreiber and Fitting, 2002)
~(k) - ~ gradkE - 2n 1 + 2~E(k)
k
(24)
with a as the nonparabolicity parameter of the energy band. The MC methods were developed many years ago by Joy (see Joy, 1995) and his programs are widely used. The work of Ding and Shimizu (e.g., Ding and Shimizu, 1996) is important here and simulations carried down to even fractions of eV were made by Fitting and co-workers (e.g., Kuhr and Fitting, 1999; Fitting et al., 2001). The MOCASIM program introduced by Reimer (1996) is also popular. Although the MC approach seems to be much more flexible and universal and enables one to model directly various phenomenological quantities, the necessary number of simulated trajectories grows enormously when any spectrum-like data need to be modeled and the computation time exceeds reasonable limits. Specific solutions to the transport equation are then sought, as, for example, in simulation of the energy spectra of BSE (Reimer et al., 1991).
IV. EMISSION OF ELECTRONS
The previous section provided fundamentals enabling one to comprehend the behavior of the electron emission excited by the impact of primary electrons. We now deal with individual contributions to the total energy spectrum of emitted electrons, shown schematically in Figure 11. This is composed of two main components, SE and BSE emission, which together form the background for electrons with characteristic energies that convey
344
M[ILLEROVA AND FRANK
------
BSE
.
.
.
.
.
Plasrnon |osses ~
AE
l
,
0 I 50 eV m
E SE
l
Ill,
,
l
Ill,
II
l
l [
l
,
l
.
l
Electron energy
,
V
--
:
l
|
l
,l
II
---
-
EmBSE Ep - - - -
FIGURE 11. Typical energy spectrum of electrons emitted under the electron beam impact (for explanation of symbols see text for details).
spectroscopic information. Secondary electron emission and electron backscattering are quite different phenomena, the first of which consists of a stream of particles released from atoms by impact ionization, the most important item within the inelastic scattering, while the latter comprises reflected primary electrons that have undergone some elastic scattering events. Nevertheless, owing to the indistinguishability of electrons, there is no way of separating these groups, except according to some statistical quantities connected with their motion after emission, i.e., with their velocity. Even when considering in simulations that the faster electron leaving the inelastic collision connected with ionization is the scattered particle and the slower is the ionization product, we do not arrive at the correct results because of the existence of processes in which the particles exchange their energies (Fitting et al., 2001). By definition, the separation between SE and BSE emission is situated at the threshold emission energy Et = 50 eV and it is believed that the tails of both distributions, extended beyond Et, compensate each other. This can be the case for high primary energies but, in the low-energy range, the compensation is far from complete, as Fitting et al. (2001) showed by simulating both SE and BSE emissions from Au (see Figure 12). Obviously, below 400 eV the BSE contribution below 50 eV (SBE) strongly exceeds the amount of fast SE above 50 eV (rise), while for Ep > 400 eV the opposite but weaker imbalance exists. This indicates that measurements of both yields, with respect to the 50 eV convention, overestimate 8 below
SCANNING LEEM
345
0.5 0.4 0.,3 0.2 0.1
"1O0
"1000 E [eV]
FIGURE 12. Contribution ~sE of fast SE (E> 50 eV) to the BSE yield ~/, together with contribution 3Be of slow BSE (E < 50 eV) to the SE yield 3, as calculated for Au. (Reprinted with permission from Fitting et al., 2001.)
a certain energy and underestimate it above the same value, while the opposite holds for r/. Nevertheless, any more correct distinction between the two emissions is possible only in simulations but can hardly be made in experiment, so from now on we continue to accept the 50 eV threshold. Naturally, when approaching the very-low-energy range, i.e., somewhere below 100-200 eV, no separation is possible and the total yield cr has to be considered. In this section we will also deal with phenomenological features of emissions such as their yields, energy and angular distributions, information depths, and (for eBSE) the coherence.
A. Electron Backscattering Emission of the backscattered electrons consists of a fraction of the electrons reflected without any significant energy loss, the eBSE emission, while the rest down to 50 eV are electrons with various energy losses. The eBSE peak is a potential source of information about the probability of incoherent elastic scattering, and hence about relations between elastic and inelastic scattering (Gergely, 1986). To acquire this information, it is necessary to measure the eBSE emission yield Tel with respect to the primary current, namely within the maximum possible
346
MULLEROVA AND FRANK
range of emission angles. Measurement on a thin-film-covered substrate under variation of the film thickness is particularly fruitful. The intensity of the eBSE peak generally increases with increasing atomic number and decreasing energy, as does the scattering cross-section Crel. Nevertheless, these monotonic dependences break down below about 1500 eV where the ~ez(E) curves for different Z start to cross each other (Schmid et al., 1983). Owing to multiple scattering inside bulk specimens in SEM, the discrete peaks connected with ionization losses are usually washed out to a smooth distribution curve of BSE modulated with low peaks due to Auger electrons (AE) and to plasmon losses. Only under special circumstances can some very weak ionization loss peaks be observed as, for example, the oxygen ionization peak for a specimen covered with a thin oxide layer; the height of this peak can be up to about 10-3 of the eBSE peak (Gergely et al., 1986). The plasmon peaks can normally be observed in electron spectra taken with an Auger electron microprobe (AEM) and used for analytical purposes as in the transmission mode in EELS. The risk of carbon contamination makes it necessary to examine discrete features in the BSE spectrum solely under UHV conditions. Although the UHV-conditioned modes are not excluded from the scope of this text, we do not consider here instruments equipped with analyzers for signal discrimination according to energy. Hence we will not further discuss the reflection EELS (REELS) method, because within the total detected BSE signal the contribution from discrete peaks is negligible. The overall shape of the BSE spectrum exhibits a very broad maximum at E~s E (see Figure 11). It represents the most probable energy loss of the emitted BSE, and in addition to scattering properties of the specimen, it depends also on the experiment geometry, i.e., on the impact and emission angles. For a tilted specimen and high emission angles (taken from the surface normal), this maximum moves toward Ep (Bauer, 1979) and the same holds for higher atomic numbers (Kulenkampff and Spyra, 1954). Reimer et al. (1991) simulated the energy spectra of the fast electron backscattering into the full half-space for layered structures and demonstrated that the position and height of the spectral maximum sensitively changes with thickness and material of the overlayer relative to substrate. Frank (1992b) presented experimental data for similar layered structures, taken in the low-energy range, together with a model interpreting the position of the BSE spectral maximum in terms of the depth of the film/substrate interface and treating the height of this maximum as proportional to the rate of quasi-elastic backscattering on the interface.
SCANNING LEEM
347
Examination of the BSE spectral maximum also requires using an energy analyzer and hence goes beyond the scope of this review, but the mere existence of this feature is important for SEM because it defines the average energy of the BSE signal species, which is crucial for their detection. Nevertheless, even for homogeneous specimens and normal impact, the mean BSE energy varies within a broad range, and is also affected by the acceptance angle of the detector. Most of the available data are taken with the cylindrical mirror analyzer (CMA) of electron energies, in which the input beam is limited between two cones with a mean emission angle of about 42 ~ In this case one gets E ' ~ s E / E P - 0.83 for A1 and 0.87 for Si but for Cu no maximum develops (Frank, 1992a). Obviously, the energy distribution of BSE should be modeled specifically for a particular detector geometry and the mean energy of BSE can move everywhere above about 0.6Ep. A crucial parameter is the total yield 7/of BSE. With the normal SEM, it is expected that rl will be nearly independent of the energy of the incident electrons and grow monotonically with the mean atomic number of the specimen, giving the broadly used material contrast in the image. Values of r/as well as its energy dependence are available from many sources but we will abandon citing individual experimental studies of the yields because near-complete experimental data from the literature have been collected by Joy (2001) into a database in which data for the low-energy range can also be found. Nevertheless, the scatter in the published data is significant, e.g., for A1 at 1 keV, six values of rl can be found in this database, spanning the interval between 0.134 and 0.2346. It is generally assumed that only the SE yield has to be measured on clean surfaces because of the sensitivity of this parameter toward surface contaminations. Nevertheless, large variations in the measured BSE yields can also be explained only by the surface status. In order to confirm this opinion, a targeted study was made consisting in careful measurement of SE and BSE yields at low energies for 24 conductive elements, both as-inserted into a UHV apparatus and after in situ cleaning by ions. The yields were measured using a device based on a principle published by Reimer and Tollkamp (1980). Here we will quote data from this study (Zadra~il and E1-Gomati, 2002), which have been only partially published hitherto (Zadra~il et al., 1997; Zadra~il and E1-Gomati, 1998a,b). In Figure 13 the data are shown for in situ cleaned specimens throughout the low-energy range down to 250 eV. Obviously, the ~(E) curves for various Z do not tend to one point at the low end of the plot as was shown in some older published results but they do this in the dataset for the as-inserted specimens; in Figure 14 we compare the "clean" and "unclean"
348
MOLLEROV,~ AND FRANK
I . . . . . . . . . .,. . . . . . .
0.5 o.4
.
.
.
,
, I
.
I
0.3 0.2
[
0.1
i
0
1
2
3
4
5
energy [keY] FIGURE 13. The BSE yields measured in UHV under normal incidence of primary electrons onto targets in situ cleaned by an ion beam; values at E - 5 keV correspond to the atomic numbers (top to bottom) 79, 78, 82, 73, 72, 74, 64, 50, 47, 41, 40, 30, 42, 29, 48, 32, 28, 24, 26, 23, 22, 14, 13, and 6 (data provided by Zadra~il and E1-Gomati, 2002). .
.
.
.
0.5
.
.
.
.
.
I
. . . .
'
. . . .
',Pt .......
: .......
'
~
. . . .
'
. . . .
I
. . . .
'
. . . .
I
,
,
,
',
',
',
i ........
Cu :
0.3
. . . .
! ........
i_
_:. . . . . . .
-: . . . .
'
. . . .
1
-Z
Agi 2;==~
i ____J---c-u----~
0.2 . ,
.
.
.
AI
,
,
,
,
,
,
,
,
"I,
,
,
,
,
,
,
,
,
,
,
~
0.1 0 0
1
2
3
4
5
energy [keV] FIGURE 14. Comparison of the BSE yields for normal impact, measured under UHV conditions for as-inserted (. . . . . . ) and in situ cleaned ( - - ) specimens; data provided by Zadra~il and E1-Gomati (2002). d a t a for several elements. It is usual to explain the o b s e r v a t i o n s as a c o n s e q u e n c e o f g r a p h i t i c c o n t a m i n a t i o n a n d oxide layers on as-inserted specimens, w h i c h b e c o m e less t r a n s p a r e n t at low energies a n d increasingly c o n t r i b u t e to the B S E signal. T h e n , b e c a u s e o f the presence o f " s t a n d a r d "
SCANNING LEEM
349
contaminations, very similar data can be obtained for different specimens, at least within their groups of a similar reactivity. Three of these pairs of measurements were studied in detail by simulation of the BSE yields from those specimens, both clean and covered by a contamination layer of a probable composition and thickness (Frank et al., 2000b). It was found that the observed differences in r/due to cleaning can be explained, for example, by the presence of a 3 nm layer of A1203.3H20 on A1 or 7 nm of carbon on Au. The question of the information depth D of BSE emission was also addressed. At a first glance, we can expect a value similar to half the penetration depth, i.e., D ~-Rx/2. Simulation showed that this is approximately so at 1 keV while at 3 keV the information depth is 2 to 4 times smaller than Rx/2 (Frank et al., 2000b) while Joy and Joy (1996) presented this depth as approximately equal to 0.2Rs. These conclusions indicate that, when entering the low-energy range, we have to consider the BSE yield as another surface-sensitive quantity and when interpreting the SEM image we should take into account data corresponding to the vacuum conditions and surface treatment used. In Figure 13 we notice that, just below 5 keV, the r/(E) curves for various Z start to cross each other, which means that the material contrast, i.e., the monotonic r/(Z) dependence at constant E, disappears here and cannot be reliably used for interpretation of micrographs in the low-energy range. This represents an additional threshold separating the low-energy range. In the SLEEM instrument the above-surface electric field has to be kept as homogeneous as possible, which restricts the specimen tilt to within narrow limits. Even so, nonnormal electron impact can occur because of relative enhancement of the radial velocity by deceleration. The BSE yield grows with the specimen tilt 4~ so that, according to MC simulations, for example at 1 keV the ratio r/(80~ ~ reaches 2.9 for A1, 2.3 for Cu, and 1.8 for Au (B6ngeler et al., 1993). The shape of r/(4~) does not noticeably vary with the energy of the electron impact. As regards the angular distribution of BSE, at high energies it is circular in the polar diagram, i.e., r/(| ~(0) cos| At energies as low as 1 keV, the same shape of the distribution was simulated for A1, but for heavier elements (Cu, Ag, Au) the distribution is more 'pointed," i.e., it increases more steeply at small | (B6ngeler et al., 1993). The same change resulted from the MC simulations of Kuhr and Fitting (1999) at 100 eV, though the Au data appeared much nearer to the cosine law than those for Ag. The eBSE distribution was found to be not only strongly pointed toward the axis but also exhibited anisotropy similar to that in Figure 3.
350
MOLLEROVA AND FRANK
B. Crystall&ity Effects In the previous section we discussed the electron backscattering from a specimen behaving like a homogeneous and isotropic continuum. Experimentally, this corresponds to amorphous substances but otherwise averaging has to be made over grains of polycrystals or different orientations of a single crystal. In practice, we usually observe details connected with anisotropy of the scattering properties of crystals. However, electron crystallography is an independent discipline with sophisticated theory and a broad range of experimental data so within this review we can only briefly touch on several key points. For very thin specimens and higher electron energies, the kinematic theory of diffraction can provide useful results, particularly as regards the geometry of the diffraction pattern from which the crystal structure and orientation can be determined; the basic relation is the Bragg equation k-
k o - - g - - g l x *1 § g z x 2* § g 3 x 3*
(25)
in which k0 and k are the wave-vectors of the incident and scattered wave, respectively, and xi* are base vectors of the reciprocal lattice, orthonormal to the base vectors xi of the Bravais lattice of the crystal. This equation represents a condition for constructive interference of waves scattered by individual unit cells in the crystal. In SEM and at low energies, large-angle scattering and multiple scattering phenomena always occur together in the signal generation so that the dynamical diffraction theory is needed. The problem consists in conversion of the incident plane wave into a wave field with the crystal periodicity. This is solved via the Schr6dinger equation with periodic potential and with the solution developed into the Bloch waves. The topic is again discussed in sufficient detail by Reimer (1998) and by authors cited therein. An important step is the development of the crystal potential into a Fourier series with complex coefficients Vu + iVg* where g comprises all points of the reciprocal lattice. The imaginary coefficients Vg* (with the dimension of energy) express the absorption of the electron waves and V0 is the (mean) inner potential inside the crystal. The Bloch waves have the formal appearance
~rj -- Z aj(g)exp[Zrti(kj + g)r]
(26)
g
where aj{g) have the periodicity of the crystal potential. The index j should run over all points of the reciprocal lattice but in practice it is sufficient to
S C A N N I N G LEEM
351
consider only n beams for which the lattice points are near enough to the Ewald sphere. The incident wave then splits into n 2 partial waves forming n Bloch waves. On substituting Equation (26) into the Schr6dinger equation, we get +
2m
Z Vhaj(g- h) - 0
(27)
he0 where K = h-l[2m(E + V0)]1/2 is the length of the incident wave-vector inside the crystal. Solution of Equation (27) gives n values of kj. and n 2 values of the amplitudes aj(g) for the incident wave K and, naturally, at least two beams should be considered of which that of g - 0 is the primary beam. It is quite obvious that the intensity of such a scattered wave is anisotropically distributed, which projects itself into anisotropy of the emitted signals so that their cosine or similar monotonic distributions become modulated. The directions ke of enhanced intensity can be estimated by the Bragg equation, now in the form of k e = K+g. Observable consequences of these phenomena include dependence of ~ on the crystallinic orientation (i.e., on the specimen tilt or on orientation of a crystal grain) and also some structure modulating the r/(| distribution. Variations in r/due to the orientation can be a source of grain contrast at polycrystals. In the two-beam approximation and assuming that the Bloch waves do not interfere, we get (according to Reimer, 1998) for variation in the backscattering coefficient
A_____9_~ = r/
~ co + ~/~g 2rtD 1 + 092- ~ / a
(28)
where ~g is the absorption length, ~g-hv/2Vg, and co=S~g is a dimensionless factor in which s = Isl characterizes deviation from the exact Bragg position (distance of the reciprocal lattice point from the Ewald sphere) and ~g = hv/2 Vg is the extinction length. Further, D is the (already introduced) information depth of the backscattered signal, D = ~I/NaB, with aB as the cross-section for scattering through angles greater than 90 ~ Because at least down to hundreds of eV D decreases with decreasing energy faster than ~g, we find that, among other effects, the grain contrast increases at low energies. Modulation of r/(| includes all the electron diffraction phenomena that have proved to be sources of extremely interesting image signals in LEEM. In the low-energy range, the Bragg angles 08 = arcsin O~/2dh~l)(with dhkt as the interplanar distance in the real crystal) are still less than 90 ~ and no
352
MOLLEROVA AND FRANK
regular diffraction pattern is formed by backscattered waves. But an important phenomenon is the formation of EBSP (electron backscattering patterns) whereby diffused BSE upon their return toward surface diffract on sets of atomic planes and form Kikuchi bands and lines, which are in fact intersections of so-called Kossel cones with the observation plane. The Kossel cones comprise all the vector directions fulfilling the Bragg equation so that one cone contains k0 and the other k, both having g as the cone axis. In EBSP these features can be visible when the backscattered electron suffers only single elastic scattering before emission. Thus, a good contrast of EBSP can be achieved solely at high tilt angles around 70 ~ and also at higher electron energies. Nevertheless, some modulation of r/(| should be present even in the low-energy range but to the authors' knowledge, no successful observation has been made yet. At energies of the order of hundreds of eV, the Bragg angles start to exceed 90 ~ and true diffraction patterns can be formed. At the same time, the penetration depth shrinks so that electrons interact with a nearly twodimensional lattice and the Bragg equation has to be fulfilled only for vector components parallel to the surface. In other words, the reciprocal lattice, normally three-dimensional with lattice points of a size inversely proportional to dimensions of the real crystal, is now filled with "rods" perpendicular to the surface. In fact the real situation is usually between the two marginal cases, so that the "rods" are modulated in "thickness" and the third-dimension condition still has to be considered. Formation of a LEED pattern with sharp diffraction spots requires the use of a beam aperture below 1 mrad as in transmission microscopy. As will be shown below, in SEM the optimum beam aperture, tuned to ultimate resolution, can approach the 1 mrad level but after deceleration to very-low-energy, the aperture grows to tens of mrad. Consequently, the diffraction spots extend to discs, as in CBED conditions in STEM. It is a matter of debate whether these mutually overlap, which would further enhance the signal. A position-sensitive multichannel detector situated above the specimen (or in a side position when a through-the-lens detection system, to which the signal electrons are deflected, is employed) enables one to observe the local deviations from fulfillment of the diffraction condition. Even a single-channel integral detector will show as brighter those areas where, at the energy used, the Ewald sphere just crosses some reciprocal lattice point. However, owing to dynamical effects, additional maxima of the signal can appear. This imaging mode will be illustrated in Section VIII. Irrespective of the beam aperture, effects connected with channeling of the Bloch functions, like formation of Kikuchi lines, take place and are visible in the phenomena outlined above, because their geometry is connected with the crystal structure and not with the beam shape.
353
SCANNING LEEM
C. Coherence within the Primary Beam Spot A crucial condition for constructive interference of waves scattered from individual atoms is coherence within the primary spot. This should be assessed in connection with the energy and angular spreads of the beam that determine whether all contributions from the illuminated spot are amplitude summed. As discussed by Buseck et al. (1988) for STEM, no amplitude addition between neighboring pixels can appear. The coherence conditions for a single static spot were discussed by Frank et al. (1999). The energy spread in the primary beam is mainly given by the type of the electron gun and varies between 0.2 eV for a field-emission cathode at room temperature up to about 2 to 3 eV for thermoemission from tungsten, provided we neglect any additional spreads generated by e-e interactions in crossovers. According to Born and Wolf (1975), the coherence condition for the path difference As, i.e., for the size Dc of the coherently illuminated area, is
Dc - I A s ] << (7,~.,2
~,~
2.45 ~
[nm; eV].
(29)
/__k/5
The initial source size, also connected with the emission type used, gives the maximum diameter of the coherently illuminated diaphragm. If we tolerate a decrease to 88% in the complex degree of coherence from the center to the edge of the illuminated area, then a quasimonochromatic uniform source of angular radius y - p/x (see Figure 15) illuminates "nearly coherently" a circle of a diameter 2r=0.16()~)/?, (Born and Wolf, 1975). Hence a further coherence condition is ,o _<
0.08(i.) ly o
~
0.98
[nm; eV]
(30)
-- lyo~
In diffraction experiments the so-called "transfer width" (see Woodruff and Delchar, 1986) plays a similar role to that of the beam coherence area. In order to understand this concept, we have to recall that the reciprocal lattice points have a "size," which is inversely proportional to the crystal dimensions. Hence the diffracted beams have a finite angular size corresponding to the dimensions of the area from which the amplitude addition takes place. If any imperfections in the primary beam exist, such as energy and angular spread, that cause a change in the wave-vector Akll, then they also correspond to some distance on a surface, just as we get the surface periodicity length from the Bragg condition, dhk-- 1/Akll. These lengths are analogously defined as w = 1/AkiN, and determine maximum distances over
354
MOLLEROVA AND FRANK
!2p
x
. . . . .
r . . . . . . .
,,-
_
! 9r
FIGURE 15. Definition of quantities used in the assessment of the primary beam coherence.
which variations in the surface periodicity can be detected. In other words, Akll represents now a dispersion caused by a finite aperture and energy spread of the illuminating beam. Thus, the area of addition of amplitudes is limited by "angular" and "energy" transfer widths Wo and wE so that
Dc
< wo
-
~. 0.61 2oe cos0 >- ot
Into; eV]
(31)
and 2E
D c < wE -- dhk ~ . AE
(32)
Later we will see that in a normal SLEEM configuration all these conditions for sufficient coherence within the primary spot can be satisfied. The diffraction spots can overlap in the radial direction when their angular size, A0 ~ )~/dhk COS0, is larger than 2or. This can easily happen and then further intensity increase is achieved. D. S e c o n d a r y E l e c t r o n E m i s s i o n
Secondary electrons are released from the target atoms by impact ionization, which forms a substantial contribution to quantities characterizing
SCANNING LEEM
355
the inelastic scattering. According to conclusions drawn from results of momentum-resolved coincidence spectroscopy, the main source of SE is decay of the valence band excitations caused by large momentum transfer spatially localized scattering events (Drucker et al., 1993). Further intensive SE generators include decay of volume and surface plasmons; the yield from the electron-electron collisions is substantially weaker. Upon release from an atom, the internal secondary electron possesses kinetic energy (taken with respect to the bottom of the conduction band) of the order of 101 eV. For example, Schreiber and Fitting (2002) studied in detail the SE emission from SiO2 and found the mean initial kinetic energy to be 13 eV. Owing to further impact ionization and cascading processes, the energy of the SE dropped below 10 eV within 10 fs. Then, scattering on phonons dominated and after 200 fs the electrons were more or less thermalized so that their energy approached 3~:T/2, i.e., approx. 40 meV at room temperature. Finally, electron-hole recombination took place and within 1000 fs the released electrons were almost all recombined or trapped. Emission of a SE has, therefore, to take place within a very short time after its generation. Data important for understanding the SE signal in SEM were reviewed by many authors, e.g., Bruining (1954), Kollath (1956), Dekker (1958), Hachenberg and Brauer (1959) and Seiler (1983). The measured SE yields are contained in the database of Joy (2001) and we will quote also the data from the study targeted at the determination of the influence of the surface cleanliness (Zadra~il and E1-Gomati, 2002). The SE yield 3 is relatively low at the energies normally used in the SEM; we can verify in the database of Joy (2001) that at 20 keV, 3 < r/for all except the lightest elements, for which both yields are roughly equal. But at low energies, 6 is significantly larger than r/--this relation creates another crucial distinction of the low-energy range. Similarly, the information depth of BSE is normally much larger than that of SE but this relation also reverses. According to the simulations of Kuhr and Fitting (1998), the relation between maxima of the depth distributions for SE and BSE from Ag is mutually opposite for electron energies 3000 eV and 100 eV. The maximum SE yield 3m, achieved at a certain energy of the incident electrons Em (located between 100 and 900 eV), remains within 0.5 to 1.7 (Seiler, 1983) or 0.6 to 2.1 (Zadra~il and E1-Gomati, 2002) for metals. For insulators, owing to the extended escape depth of SE, the yield can reach values even higher than 10 (Seiler, 1983; Joy, 2001), for alkali halides in particular. In Figure 16 a set of data similar to that in Figure 13 is given; these are now values of 6 for the same selection of 24 conductive elements.
356
Mf]LLEROV~t AND FRANK
2.0
5 1.5 1.0 0.5
0
,
,
,
,
,
,
,
,
4
5
2
1
3 energy [keY]
FIGURE 16. The SE yields measured in UHV with normal incidence of primary electrons onto targets in situ cleaned by an ion beam; values at E = 1 keV correspond to the atomic numbers (top to bottom) 64, 13, 40, 78, 79, 72, 47, 30, 82, 50, 14, 29, 24, 48, 74, 73, 28, 32, 42, 26, 22, 41, 23, and 6 (data provided by Zadra~il and E1-Gomati, 2002).
i i ii[i ii i ii i ii
2.0
5 1.5 1.0 0.5
i
0
,
, ~
,
,
,
,
,
,
,
,
,
,
4
5
1
{
2
3 energy [keV]
......
=
FIGURE 17. Comparison of the SE yields for normal impact, measured under UHV conditions for as-inserted (. . . . . . ) and in situ cleaned ( - - ) specimens; dashed curves correspond to (top to bottom) Ag, A1, Pt, Cu, and C at 1 keV (data provided by Zadra~il and E1-Gomati, 2002).
SCANNING LEEM
357
Further, in Figure 17 the same pairs of measurements are given as in Figure 14, i.e., for the specimen as-inserted into UHV and after being ion-beam cleaned. Here we notice a pronounced similarity between the as-inserted curves, which obviously corresponds to similarly contaminated surfaces although the specimens were thoroughly precleaned and measured under clean conditions. A semiempirical theory of SE emission, summarized by Seiler (1983), gives a universal (i.e., specimen-independent) curve
3m-- "
~
1--exp
--2.3 Emm
"
(33)
It is also stated that for metals, 8m/E m is constant (due to the proportionality of both quantities to j4/5) and approximately equal to 2 x 10-3 eV -1 (Ono and Kanaya, 1979). Nevertheless, data tabulated by Seiler (1983) do not indicate constancy of 3m/Em and when extracting this ratio from Figure 13, we find that its average value is around 0.002 eV -1 but the values are scattered between 0.0012 and 0.0053 eV -1. All sources of data confirm that in their Z dependences both ~m and Em exhibit a modulation corresponding to the periodic system of elements. This modulation is apparent even when drawing a 6(Z) curve for an arbitrary energy value (Zadra~il and E1-Gomati, 1998b). At incident electron energies sufficiently higher than Em, the SE yield decreases as E -~ (Drescher et al., 1970), which is the energy dependence of the Bethe stopping power. Near and below the yield maximum, no universal relation exists except Equation (33). The energy distribution of emitted SE has a strong maximum at energy E~E (see Figure 11), which is smaller for insulators than for metals, for which it moves between 1 and 5 eV, while the width of this distribution, measured at half maximum, ranges from 3 to 15 eV (Schfifer and H61zl, 1972). Ding and Shimizu (1996) verified that the energy distribution does not depend strongly on the emission angle. The dependence of the position and width of the distribution peak on the material and its surface status were studied by Dietrich and Seiler (1960) and Joy (1987), and others. Fitting et al. (2001) found, again for SiO2, that the value of E~'E decreases with increasing escape depth of SE. Chung and Everhart (1974) presented a simple theory leading to a relation for ~(EsE) for metals. They supposed the surface potential barrier fully transparent for EsE> 0 (with EsE measured from the vacuum level) and nonpenetrable otherwise, and the SE generation to be isotropic and depth independent. The resulting
358
MfJLLEROVA AND FRANK
expression was
dNsE dEsE
~ = K - -
1 ESE E (EsE + q~W)4
(34)
(where 4~w is the work function and K is a material constant), giving E'~E -- 4)w/3. For our next considerations, we need some "mean" energy of SE; from Equation (34) the mean value of ESE is 2 4~w. However, the mean
value overestimates the contribution of fast SE so that it is more reasonable to take the median, which is equal to 4~w here. Thus, for detection considerations, we can use 3 to 5 eV as the typical energy of SE. A more exact theory would require incorporation of processes of SE generation, diffusion inside the target, and penetration through the surface barrier. Reimer (1998) reviewed calculations made for aluminum (see, e.g., Bindi et al., 1980) and hinted at anisotropy of the internal SE release, which is afterwards quickly randomized, owing to the short mean free path, to the cosine distribution. In practice, the distribution 8(| cos | is observed generally at all instances (see, e.g., Kanaya and Kawakatsu, 1972). Nevertheless, with single crystals some structure again appears on the angular distribution, caused by channeling of the Bloch functions as we mentioned for the BSE emission (see, e.g., Burns, 1960). The smooth energy distribution described by Equation (34) can exhibit some additional structure at energies equal to energies of plasmons. Everhart et al. (1976) observed this structure with aluminum and for an atomically clean surface they found that the energy distribution was broadened and contained some features at energies corresponding to surface and volume plasmons. Nevertheless, after very slight oxidation the structure not only disappeared but also the main peak became much narrower. This indicates that the SE generation via decay of plasmons is sensitive to the surface status and is much weaker at "real" surfaces. At high energies the dependence of 8 on the specimen tilt angle 4~ is very important, causing the most pronounced contribution to the image signal, owing to which the SEM image acquires its three-dimensional appearance. The proportionality can be written as 8(4~)oc secn 4~ with n decreasing from about 1.3 to 0.8 throughout the Z scale (Seiler, 1983). An extreme demonstration of this dependence is so-called edge effect, i.e., a strong overbrightening of side walls of surface steps that dominates micrographs at conventional energies. The phenomenon is simply caused by the SE escape depth being shallower than the penetration depth of primaries, owing to which any inclined facet represents an additional emitting surface. Thus, the edge effect should disappear at low energies (see Figure 18) near to Em for the maximum SE yield where all generated SE are emitted; this was
SCANNING L E E M
o 0 . 5 keV
C) ,._.,.
9 0.5 keY
AI
9 1 keY 9 2 keY 9 5 keY
I3
0J
0
'J
LI'iIIj
20
Au
9 1 keY 9 2 keY 9 5 keY
13oo
9 10 keY
1 .t.,,_.=.=i--.=~
359
9 1 0 keY
.-e~'2
-
J
40
J
tilt angle (I) [deg]
J--
60
j
'
80
0
0
'
J
20
'
4
b
'
60
tilt angle (I) [deg]
FIGURE 18. Experimental data for tilt-angle dependence of the SE yield. (Reprinted with permission from B6ngeler et al., 1993.)
quantitatively verified by Pejchl et al. (1993). Consequently, the SE contrast at low energies is restricted to the "shadowing" connected with the usual side position of the detector and the image becomes more "flat" (see Joy and Joy, 1996). When exciting SE from a single crystal, the monotonic 3(4~) dependence again acquires a structure. This is normally comparable with that of the BSE yield, A~/r/ (see comparison made for Si(111) by Seller and Kuhnle, 1970) but toward low energies A3/3 does not grow so distinctly as A~/~ does. Hence any grain contrast in SEM micrographs at low energies are more probably caused by the BSE emission anisotropy. Further studies regarding the angular distribution of 3 include those of Salehi and Flinn (1981) and Libinson (1999). An important collection of experimental results concerning the SE emission anisotropy has been acquired by using UHV SEM instruments equipped with detectors featuring an enhanced angular sensitivity, usually achieved by suppression of SE emitted off the direction toward the detector. Then, Homma et al. (1993) observed alternating 2 x 1 and 1 x 2 domains in subsequent atomic layers on Si (100) as well as reconstructed 7 x 7 domains coexisting with nonreconstructed remains of 1 x 1 phase on Si (111). Domains were visible even at an electron energy of 25 keV but enhanced contrast was demonstrated at 2 keV. Similar instrumentation was used to visualize surface atomic steps, e.g., those on Si (111) (Ishikawa et al., 1985) or on an oxidized Cu surface (Bleloch et al., 1989). Obviously, with careful in situ treatment of the specimen surface, even in the "incoherent" SE imaging many phenomena can be observed which would intuitively be
360
MULLEROV!i. AND FRANK
expected to be perceptible solely by diffraction contrasts in the LEEM method. An important characteristic is the mean escape depth )~esc of SE, which governs the information depth of the SE image. The probability of escape Pesc is generally considered to be exponentially dependent on the depth, i.e., Pesc~ exp (--Z/~,esc). Values of ~esc range between 0.5 and 1.5 nm for metals and between 10 and 20 nm for insulators while the maximum escape depth is T TM 5Le~ (Seiler, 1967). The larger values of Le~c for insulators are in accordance with the enhanced SE yield from them. Fitting et al. (2001) found for SiO2 that ~esc decreases with increasing SE energy--for EsE < 3 eV it amounted to about 10 nm while for Ese > 20 eV it dropped below 1 nm. If the escape depth is brought into relation to the electron range R, we get the maximum SE yield at R-2.3Xesc (Seiler, 1983). At higher energies the SE generation extends to depths from which no escape is possible while at lower energies the generation rate (the integral of the stopping power along trajectory of the incident electron) diminishes. The shallow escape depth, together with sensitivity toward ionization energies of least bound electrons, makes the SE emission very sensitive to the surface status, its cleanliness and contamination, and also to the radiation damage. At conventional SEM energies, the secondary electron signal is composed of so-called SE1 and SE2 contributions, the first being excited directly by PE while the latter are due to BSE returning toward the surface. While SE1 escape from an area the diameter of which is approximately (d2 + ~e2sc)1/2 with de as the primary spot size (see, e.g., Everhart and Chung, 1972), the SE2 signal emission spot is broadened by lateral diffusion of BSE so that the specimen response function consists of two bell-shaped features of different width. We will discuss this later in connection with the image resolution but now let us mention that the total SE yield is usually written as
(~ - - ~ P E + ~ B S E - -
~0[secq~ -+- fl(q~)~]
(35)
where 30 is the SE1 emission at normal impact of PE and fl(~b) denotes the ratio of the SE yields between PE and BSE. The ~b dependence of I3 is decreasing (Seiler, 1983) and /3> 1 because BSE have lower energies than PE and also their trajectories are generally more inclined with respect to the surface normal. Above about 10 keV, we get fl~-2.5 with only weak material and energy dependences. For low energies, when the electron range approaches the escape depth of SE, this approach, as well as any distinction between SE1 and SE2, becomes questionable. Nevertheless, at least at the beginning of the low-energy range, i.e., down to, say, 2 to
SCANNING LEEM
361
3 keV, Equation (35) can be considered, probably with an increasing value of/~. The role of BSE in the SE emission has been studied by numerous authors (e.g., Kanter, 1961; Kanaya and Kawakatsu, 1972; Joy, 1984; Hasselbach and Krauss, 1988; B6ngeler et al., 1993). For us the distinction between SE1 and SE2 is of minor importance because in SLEEM the standard detectors acquire the total emission cr = • + r/. Nevertheless, we should be aware that, even at low energies, the SE yield from surface films depends on the underlying substrate and when the two materials have very different Z, the change in 3 with the film thickness is very strong so that in fact the SE2 contribution prevails over that of SE1, see, e.g., measurements of Thomas and Pattinson (1970). As regards the noise in SE emission, it is usually considered to follow the Poisson distribution. This was proved for energies below 250 eV (Seiler, 1983) but at higher energies some excess noise content is found (see Reimer, 1971) because of the SE2 contribution. This question does not seem to have been fully answered. Finally let us mention that SE emitted from ferromagnetics are spin polarized (Kirschner, 1984). The degree of polarization is nonnegligible even for very low-energy electrons and further increases with E, with the highest polarization found for the slowest SE. The effect is explained by the different reflectivity of electrons with different spin orientations. This phenomenon would enable one to observe the domain contrast if a detector of polarized electrons was available.
V. FORMATION OF THE PRIMARY BEAM
We have already touched on the important circumstance that in SEM the specimen represents a part of the imaging system. The information collected, coming from the entire interaction volume of the primary beam, is ascribed to a single point labeled by pixel coordinates so that the response function of the specimen, i.e., distribution of the signal excited by a monochromatic infinitely narrow incident pencil, has to be taken into account when assessing the resolution. However, incorporation of the specimen properties prevents us from drawing general conclusions about the instrument quality so that it is usual to evaluate an "intermediate" quantity, namely, the current distribution in the primary beam spot entering the specimen. We will do the same and afterwards we extend the discussion toward the concept of the "real" resolution on a particular specimen.
362
MULLEROVA AND FRANK
A. The Spot Size
Within the scope of this text, we cannot go into details of the electron optical theory of the SEM column, of the lens aberrations and their combinations, and related problems. Let us only mention that correct results, particularly for coherent or nearly coherent illumination by various types of field-emission guns, can be obtained only by wave-optical theory of the electron probe formation, which regards lenses as diaphragms filled by a phase shifting medium that deforms and trims the wavefronts. However, our aim is to explain, using relations as simple as possible, the specifics of the low-energy spot formation and hence we will utilize the simplest approximate figures obtained from geometric optical theory. For more details we can refer to Reimer (1998) and particularly to an exact analysis of the topic made by Hawkes and Kasper (1996b). We will simply consider the primary spot as a convolution of the current distribution within the demagnified image of the gun crossover with discs of confusion of the basic aberrations. Assuming the astigmatism and defocusing aberrations fully corrected, we take into account contributions to the spot size expressed in the form of discs of confusion the sizes of which are
dG --
41) 1/2Of-1 ,
~
ds - KsCsot 3,
AE dc - K c C c --if- or,
do - KD~.Ot-1
(36) where dc is the demagnified crossover, ds, dc, and do are the discs of spherical, chromatic, and diffraction aberration, respectively, I is the beam current, /3 is the gun brightness, ot is the specimen-side angular aperture of the primary beam, Cs and Cc are the coefficients of spherical and chromatic aberration, respectively, and Ks, Kc, and KD are numerical factors dependent on the model of the spot formation. Here the leastconfusion planes are assumed for spherical and chromatic aberrations and the final aperture-limiting diaphragm is considered uniformly illuminated. When using the full beam diameters in the least-confusion planes of spherical and chromatic aberrations and FWHM of the Airy disc for the diffraction aberration, we get the numerical factors as Ks = 0.5, K c = 1, and KD=0.6. The next step is to select a summation rule for combining the contributions from Equation (36) into the overall spotsize de. It is traditional to consider the ray radii in the individual discs as mutually independent random variables with normal distributions. Then the
SCANNING
LEEM
363
summation rule is given by a convolution of Gaussian functions the result of which is also Gaussian and
4=4+4+4+d
.
(37)
In fact, the individual contributions are neither independent nor normally distributed so that Equation (37) provides only a rough estimate of dp. A more realistic but still reasonably simple relation is obtained by defining the disc sizes as the diameter encircling some current fraction. Using this approach, Barth and Kruit (1996) derived the summation rule (for 50% of encircled signal) 1.3/4 . --1 3 2/1.3
+d 2
(38)
and determined modified values of the numeric factors, namely Ks-O.18, Kc-- 0.34, and KD -- 0.54. Other summation rules exist that provide more exact but at the same time more complicated relations for the spotsize (see, e.g., Kolafik and Lenc, 1997) but we shall use the summation rules in Equations (37) and (38) and compare their results. First of all let us make the following simple observation: when the electron energy E decreases, the wavelength increases as )~o(E -1/2. This causes the Airy disc to extend and in order to suppress the impact on resolution, we have to adjust the beam aperture to the same slope ot c~ E -1/2. But then the spherical and chromatic aberration discs grow as dsoc E -3/2 and also dc oc E -3/2. The same energy dependence would in turn apply to the total spotsize dp, fully preventing any use of very low energies. To compensate this, an objective lens would be needed with aberration coefficients, Cs and Cc, proportional to E 3/2. However, the normal magnetic lenses have energy-independent aberration coefficients. It is true that, for example, for weak lenses Cs is proportional to f3 (Glaser, 1952), i.e., in fact to E 3, but after changing the beam energy we have to refocus to the same specimen plane and hence to get the same f and also the same Cs. Consequently, the spotsize enlarges at low energies. The optimum angular aperture Otoptfor achieving the ultimate resolution d~' is simply calculated from the relation adp/aot-O. In Figure 19 we have the function Otopt(E) plotted from the beam energy 15 keV downwards for both above-given summation rules and for two model SEM instruments of a different quality. These are defined in order to span the current instrumentation scope; the first, "TEG SEM," represents old instruments probably not marketable any more but still serving in plenty of laboratories
364
MI]LLEROVA AND FRANK 9
9
9
|
.
.
.
.
.
.
i
,
9
9
,
9
!
,
101 FEG
-o
'
..-H''"
:
s ; ' "
t,-
E
,.__,
m ,--1 0 0 1E (D Q.
10 -1 10 -3
I
10 -2
i
i
10 -1
9
10 0
.
9 i
101
energy [keV] FIGURE 19. The optimum angular aperture, Olopt,for the smallest spotsize, plotted versus electron energy. TEG SEM and FEG SEM denote the two sets of SEM parameters given in the text, the dashed line corresponds to the summation rule (37), and the full line to the rule (38).
while the other, " F E G SEM," is for high-quality modern devices. The parameters were chosen as /3-105 A cm -2 sr -1, I - 5 pA, A E - - 2 eV, C s - 50 mm, C c - - 2 0 mm for TEG SEM, a n d / 3 - 109 A cm -2 sr -1, I = 100 pA, A E = 0 . 2 eV, Cs= 1.9 mm, C c = - 2 . 5 mm for F E G SEM. Naturally, there might be queries about individual parameters but as we will see, the basic trends that we are now seeking for are independent of these details. One general trend is obvious already from Figure 19: along the low-energy range, all curves progressively acquire the same slope Otopt(xE 1/4. T h i s behavior can be easily obtained from Equation (37) when we retain in it only members growing at low energies, i.e., dc and dD. When substituting ot c~ E 1/4 into all terms listed in Equation (36), we get the proportionalities dG (X E -1/4,
ds (x E 3/4,
dc (x E -3/4,
dD (x E -3/4
(39)
so that the influence of dc and dD dominates and hence the same slope can be expected for de. In Figure 20 is shown the dp (E) plot for ot = Otopt,which confirms the said behavior, again independently of the summation rule and instrument parameters. The foregoing very simple considerations have yielded the general relation for SEM, namely the proportionality of the spotsize to E -3/4. This says that when we want to turn from the conventional energy like 15 keV to units of eV, the resolution in nanometers deteriorates to the same number
S C A N N I N G LEEM
365
104 103 rE ~
N
10 2
O ~
10
100 ,
10-3
,
,
|
10-2
,
,
,
|
,
,
,
I
1'0-1 100 energy [keY]
,
,
,
,
1;01
FIGURE 20. The ultimate spotsize, d~', for the optimum angular aperture Otopt, calculated for two sets of SEM parameters denoted by TEG SEM and F E G SEM (see text) from the summation rules (37) ( . . . . . . ) and (38) ( - - ) .
in micrometers, i.e., below the level of a standard optical microscope. The proportionality to E -3/4 s e e m s to be broken by parameters of some recent microscopes that guarantee the spotsize at 1 keV only about three times larger than that at 15 keV but the improvement is achieved at the cost of shortened working distance, reduced current, and other restrictions (see, e.g., Nagatani et al., 1987). In general, a conventional SEM without aberration correctors can work at acceptable quality of micrographs down to 1 keV. Because the E -3/4 slope does not depend on the instrument class, we will not discuss in detail the methods of optimizing the objective lenses and detection systems toward improved resolution at low energies. These mostly rely on placing the specimen very close to or even inside the magnetic field, which in turn brings some limitations on other parameters of the microscope operation. Among possible configurations, the so-called single-polepiece lens (Mulvey, 1984), with the second polepiece shifted far from the optic axis and the primary spot, attracts the most attention. Various configurations based on the single-polepiece principle were studied by Pawley (1984), Bode and Reimer (1985), Shao (1989), Mtillerovfi et al. (1989) and Ximen et al. (1993), and others. Some setups achieved very low aberration coefficients like the Cs=O.15 mm and C c = 0 . 5 5 mm of Tsai and Crewe (1998).
366
MOLLEROVA AND FRANK
B. Incorporation of the Retarding Field A qualitative step forward as regards possibilities of the SEM operation throughout the full energy scale was achieved by introducing nonconstant beam energy along the column. The idea is to form and transport the beam at high energy and only close to the specimen to retard it to a final low energy. The underlying principle consisted in one property of the immersion electrostatic lenses, namely that the magnitude of their aberrations corresponds to the higher of the electron energies on either side of the lens. So an immersion lens, i.e., an electrostatic lens with different potential on the marginal electrodes, can be inserted into the end part of the column with the negatively biased electrode toward the specimen. Fundamentals about configurations utilizing this principle were studied in detail by Frank and Mfillerovfi (1999). For estimation of aberrations of the immersion lens we use the approximate equation (Lenc, 1995)
1fzil[(I)~z)]1/21(I)~Z o0]
Cs ~ Cc ~-~
)
~
dz
(40)
where interval (z0, zl) spans the transition region of ~(z) between ~0 and ~1. If we consider the electrostatic field strength abruptly changing in the planes of flat electrodes held on ~0 and ~l, we get
Cs ~ Cc ~
g + ( ~ / _ ~ + 1) 2
1-
(41)
(see also Lencovfi, 1997) with w and 1 being the distances between the specimen and the first electrode and between electrodes, respectively, and k the ratio of electron energies on either side of the lens, i.e., k = Ee/E (Ep is the beam energy in the SEM column and E = Ee + e Ub, with Ub being the retarding potential, is now the lowered energy of impact on the specimen). In Figure 21 we see that the approximation (41) differs appreciably from results obtained when substituting real potential distributions into Equation (40) but on its basis we still can make at least one simple consideration. At very low energies, i.e., for high values of k, both Cs and Cc approach w/2. So they are still independent of energy but can be quite small. However, for w small enough both coefficients are approximately proportional to Ilk = (l/Ee)E and hence diminish with decreasing energy, as we required in the previous section. Of course, the aberrations according to Equation (41) combine with aberrations of the magnetic objective lens but
SCANNING LEEM 10 0
.....
---
......
---
.....
367
; - - - - - -:- - - - - - - - -ii
Cs/I
~.r""
Cc/I
f
C Jl
,
,
1 0 -1
10 -2 |
i
,
0.3
|
,
0.6
,
,
0.9
i
1.2
working distance, w/I
FIGURE 21. The aberration coefficients, Cs and Cc, of the immersion electrostatic lens plotted versus the working distance w with both axes scaled by the length of the retarding field I. (a) Approximate Equation (41) for abrupt field transitions; (b) and (c) calculation from Equation (40) for real potential distributions with the first electrode (nearest to the specimen) of a thickness t--0.1 l (b) and t =0.2 l (c). those are in the summation rule weighed by k -3/2 o(E 3/2 (Lencovfi, 1997), which is exactly the energy dependence that fully suppresses the resolution worsening at low energies. Obviously, the immersion objective lens eliminates deterioration of the objective lens parameters for slow electrons and introduces its own but weaker tendency to a larger spotsize. Figure 22 shows the most popular design of a compound lens consisting of the magnetic focusing lens and electrostatic retarding lens (Frosien et al., 1989), which is, together with the above-lens detector, also called M E D O L (magnetic-electrostatic detector objective lens). Authors report improvement in the aberration coefficients from C s = 59 mm and C c = 15 mm to C s = 3.7 mm and C c = 1.8 mm at the immersion ratio k - 1 7 so that a resolution of 5 nm at 500 eV was achieved (Martin et al., 1994). This design was also used in the first and still the only commercial SEM with the retarding field element and subsequently its parameters have been further upgraded. With a similar configuration, Knell and Plies (1998) obtained 3 nm at 1 keV and 9 nm at 200 eV. The MEDOL-type lens was preceded by a purely electrostatic (three-electrode) lens by Zach and Rose (1988), called E D O L (electrostatic detector objective lens, see Figure 34); further data were then published by Zach (1989) and Zach and Haider (1992). For a beam energy of 8 keV inside the column, they applied the electrode potentials-7.5, + 7, and 0 keV (when proceeding from the specimen) and
368
MULLEROV]i AND FRANK
i~ ~ ;~.....
specimen
FIGURE22. Combinedmagnetic-electrostatic (compound) objective lens. (Reprinted with permission from Frosien et al., 1989.) hence reached a landing energy of 500 eV for which a resolution of 7 nm was reported. Other configurations on a similar principle include the use of a so-called "booster," i.e., a tube around the optic axis between the anode plane and the lower polepiece of the objective lens, insulated and held at a high positive potential (Beck et al., 1995) so that its lower end fully corresponds to the arrangement in Figure 22. Preikszas and Rose (1995) explored the possibilities of optimizing compound lenses and took into account maximum feasible magnetic and electric fields (they considered as limiting values 5 k V m m -1 and 1 T), tolerable fields at the specimen surface, bore diameters in electrodes and polepieces, maximum immersion ratio, and energy spread in the beam. Also Khursheed (2002) examined the aberrations of a set of the compound lens configurations. Let us only briefly mention that, adjacent to the SEM instrumentation area, is the family of IC testers, i.e., specialized scanning devices for inspection of semiconductor structures and measurement of critical dimensions on them (see, e.g., Ezumi et al., 1996). Their recent versions nearly exclusively work in the low-energy range around 1 keV, employ
SCANNING LEEM
369
various combinations of the compound lenses with energy filters (e.g., Frosien and Plies, 1987) and detectors, and achieve resolution comparable with those mentioned above. Practice has confirmed the advantages of using the retarding field principle, i.e., immersion or compound lenses, for SEM in the low-energy range. In recent commercial instruments acceptable imaging parameters have been achieved down to about 200 eV and the limit for reported laboratory configurations and IC testers is similar. A separate class is formed by the first operated versions of aberration correctors. These are capable of achieving the resolution quoted above even in a device with the beam energy constant within the column. Possible corrector configurations were reviewed by Rose (1987), Rose and Preikszas (1992), Hawkes and Kasper (1996a) and Hawkes (1997). The aberration correctors are, nevertheless, mostly applied to STEM, TEM, and LEEM instruments where the specimen influence on the real image resolution is either nearly negligible or does not apply so that any spotsize correction is more efficiently projected into the final result. Only a few applications in SEM have been reported yet; these were briefly reviewed by Frank (2002). C. The Cathode Lens In the previous section we noticed that for a very short working distance w of the retarding immersion lens, the aberration coefficients diminish with decreasing electron energy. A promising alternative is thus to choose w = 0, i.e., to apply the retarding potential directly between the specimen and some anode placed closely above. This configuration is called a cathode lens (CL) and has been known since the beginnings of electron microscopy as the crucial component of the emission electron microscopes. As we already mentioned in Section I, Recknagel published the fundamental theory of this optical element as early as 1941 and showed that its basic aberrations are proportional to the ratio of the initial and final electron energies. The same should be expected for the reversed function in the SEM and this is indicated by Equation (41). More exact analytical relations for Cs and Cc for a combination of the cathode lens with the focusing magnetic objective lens with aberration coefficients Cf and Cfc were derived by Lenc and Mtillerovfi (1992b): l CS-k-~
E ( 'J~ 3 1)4 1 (k 1)2)3 1 + ~ (4~+1 v~§
+
\
2--v~
(42)
370
MULLEROVAAND FRANK / CC =
k3/2
( k - 1)2 {3~/kk- 1 1) 3 - K 2~/k
(43)
(~/--k+
with D as diameter of the anode bore. Instead of an abrupt potential transition in the electrode plane, the quadratic polynomial shape was considered here. For our simple characteristics of the energy dependences, development of Equations (42) and (43) into a power series for large k (i.e., small E) gives relations that are easier to grasp:
/
C s ~- -~p E +
Cc ~
(~
81
)
l E3/2
+ -i-~ Cfs E 3/~---
1 9 Cf E3/2 Ep E -+--~-fi}~ +... ~p
+
~ ~ ~
(44)
Equation (44) confirms the conclusions of the previous section: the immersion lens introduces the E 1 slope for both spherical and chromatic aberrations but eliminates the energy dependence of the focusing lens aberrations via the weight proportional to E 3/2. The same holds for the "aperture lens," i.e., the optical power of the CL field penetrating the anode bore and forming a divergent lens, as we will discuss below. If we now substitute Equations (42) and (43) into Equation (36), then into Equation (38), and finally calculate again the optimum aperture Otopt, we obtain the results shown in Figure 23. (In this section we complete the sets of model parameters, FEG SEM and TEG SEM, with D = 3.5 mm, E p = 15 keV, and l = 1.5 and 15 mm.) We see that the optimum angular aperture in the specimen plane is, at least at lowest energies, proportional to E -1/4. When substituting this into all four contributions to the spot size (Equation (36)), we get both da and ds proportional to E 1/4 while both dc and dD scale as E -1/4 and this can also be expected for dp. Because previously we found that these basic proportionalities are the same for both summation rules, with Equation (38) simply providing 1.6 times larger aperture and 1.8 times smaller spotsize, we used here only one rule. It is important to note that the optimum angular aperture just below the focusing lens, i.e., the beam aperture ac formed by the microscope column, remains nearly the same when switching the cathode lens on. Hence the SLEEM mode does not require any significant realignments of the column. In Figure 24 we see again a comparison of the calculated ultimate spotsizes, d~, for two sets of the SEM parameters as defined above; the summation rule (38) was used again. Obviously, the slope E -1/4 is actually achieved at low energies, namely in the energy range where the higher
S C A N N I N G LEEM
i
.
.
.
.
i
.
.
.
.
.
.
.
.
.
.
371
.
.
102 [ TE;.I~)="T:eFEG'-.1...... ~,""-.......
:
i----i
-o
: TEG~r . . . .
t_
E
101
10~
t ....
. . . . . . . . .
""~""'.ff..''""+22"".-...
, . . . . . . . . .
. :..;,,,:~.'~1-o
.-':~
i"
. . . . . . .
i
|
-
:
-"'""-
,=-
........
..~-.~:~
i
|
"
|
-
i_
. . . . . . . . . . . . . . . . . . . . .
|
|
,
i
,
,
i
.
,
|
,
,
,
i
,oo
energy [keY] FIGURE 23. The optimum angular aperture, ~opt, for the smallest spotsize, plotted versus electron energy for a CL-equipped SLEEM. T E G SEM and F E G SEM denote the two sets of SEM parameters given in the text; the summation rule (38) was used with Cs and Cc substituted from Equations (42) and (43), respectively. For the cathode lens mode, the aperture is shown both between the focusing and cathode lens ( - - 9 9) as well as in the specimen plane ( . . . . . . ); for the latter case the aperture without CL is also shown ( ). The numeric labels denote the maximum field within the CL in kV mm -1.
members in Equation (44) become negligible. For larger aberrations of the focusing lens this happens at lower energies so that, quite paradoxically, the overall drop in resolution between the primary beam energy and, say, 1 eV is smaller for the lower quality device--for the TEG SEM and 10 kV mm -], these spotsizes are identical in Figure 24. Figure 24 demonstrates one crucial fact: below some threshold of the order of hundreds of eV, even the routine microscope, equipped with the cathode lens, surpasses the top-quality device as regards the image resolution. This advantage is paid for by the fact that the specimen has to be immersed in the electrostatic field, the strength of which governs the spotsize. The optimum aperture varies with energy and is therefore not convenient to use when acquiring a series of micrographs typical for the SLEEM operation, i.e., showing the same field of view over a broader energy range. In this case some fixed angular aperture is adjusted and it is interesting to enquire how this modifies the resolution vs. energy curve. In Figure 25 we see that when fixed apertures are chosen from among those optimum for certain energy within the low-energy range, deterioration at higher energies
372
MOLLEROVA AND FRANK
9
"i.,,~
..
.
.
,,,
10 3
,
.
.
.
!
,
- ..~:, ,
,.-
~ ,
~ ",,,.
.
.
.
,
i
.
.
. . . . . . . .
: . . . . . . . . . . . . . . . . . . . . . ,
TEG
i
,
".
" . ~
.
,
,
~,
,
"~ 10 2 t,_._,
N
.m U~
O l
e~
i "----.i
01
if)
10 0 10 -3
10 -2
10 -1
10 0
101
energy [keV] FIGURE 24. The ultimate spotsize, de", for the optimum angular aperture Olopt, calculated for the two sets of SEM parameters denoted by TEG SEM and FEG SEM (see text) from the summation rule (38): the conventional SEM mode without CL (. . . . . ) and the SLEEM mode with the CL excited ( - - ) , namely for the maximum field strength labeled in kV mm -1.
9 . . i
.
.
.
.
.
.
.
.
~' 101 t"
..........
(I.)
1 2 ~ -
N o0
o Q. t,/)
10 0 I
10 -3
10-2
10 -1
10 0
101
energy [keV] FIGURE 25. The ultimate spotsize, dp m, for the optimum angular aperture ~opt, calculated for the model FEG SEM parameters (see text, maximum CL field 10 kV mm -1) from the summation rule (38) (. . . . . ), together with resolutions obtained for three fixed angular apertures, namely 1, 2, and 4 mrad ( - - ) .
SCANNING LEEM
magnetic
Ep
373
f
polepieceof OL
focusing lens
magnetic shielding
6-segment semicond. detector .. ._/~
____~__ __ ....
vl..1~
i
Ub
i
;:
specimen .I/
. . . . ~_
polepie~,~ ! ~Jens specimen
ofSPL "~==._ v////////////////a t~IPA ~\\\\\\\\\\\\\\\"~ -
"[~~~~/'
m
(a)
(b)
FIGURE 26. (a) Simplest configuration of SEM with the cathode lens introduced below the objective lens; (b) single-polepiece magnetic lens (SPL) installed below the specimen and serving as the focusing lens while the original objective lens is either switched off or used as an additional condenser lens (in the SLEEM mode, the anode/detector assembly was radially inserted from side to below OL).
is moderate only and, in some instances, a resolution really constant throughout the energy scale is obtained. In the previous paragraphs we concentrated on simple relations concerning the energy dependences of the beam aperture and spotsize. We assumed the electrostatic and magnetic fields of the immersion and focusing lenses as nonoverlapping and, furthermore, the shapes of electrodes and polepieces have not been taken into account. The simplest arrangement, shown in Figure 26(a), can be also realized via adaptation of a conventional SEM (Mtillerovfi and Frank, 1993), as will be mentioned below. An electrostatic focusing lens was used in LEEM by Liebel and Senftinger (1991) while Mtillerovfi and Lenc (1992b) applied to SLEEM the singlepolepiece magnetic lens (see Figure 26(b)). Khursheed (2002) compared the ultimate resolutions achievable in three configurations that included the specimen inserted into the magnetic field without any retarding, and both the nonoverlapping and overlapping magnetic focusing and electric retarding fields. Using a simple model of very thin electrodes and the bellshaped magnetic field (Glaser, 1952), he found that the overlapping fields provide 1.5 to 2 times smaller spotsize than the "sequential" configuration
374
MULLEROVA AND FRANK
and at 5 kV mm -1 a spotsize of about 1 nm for an electron energy of 200 eV was calculated.
D. The Pixel Size As we already mentioned in Section IV.D, the specimen response function for the total electron emission is composed of two bell-shaped contributions of different widths. The narrower peak corresponds to the SE1 part of SE, released directly with primary electrons, and its width is similar to the primary spotsize dp, amounting approximately to (d2+)~2s~)1/2, while the broader component is that of SE2 and BSE and its width is similar to the electron range R. At high energies, the SE and BSE signals are, as a rule, detected separately and the SE resolution is much higher than that of BSE. The SE2 contribution to the SE image is usually smeared so much that visually it is not apparent and when the resolution is measured between 25 and 75% of the signal rise on a sharp edge, the SE2 signal need not manifest itself at all. The BSE resolution is usually presented on small clusters of heavy metals so that the localization of information is improved by a sharp structure within the broad three-dimensional distribution of the BSE yield. However, at low energies the electron range approaches the escape depth of SE and the widths of both response functions become similar. As demonstrated for a silicon specimen by Reimer (1998), below 1 keV the SE distribution becomes even broader than that of BSE owing to lateral diffusion of SE2 after their release by BSE. In the SLEEM method, we usually detect a mixture of SE and BSE and use just the energy range where both distribution widths are comparable--this is why we have to consider the real resolution, or the pixel size, as determined by the full response function incorporating also the specimen. The problem was solved using the response function formalism by Frank (1996a,b). The spatial distribution IT(r) of the total emitted current in the surface plane can be written as
I T ( r ) / I p -- 8 C ( r ) +
r/(1 +/38)
f
r,)dr'
(45)
where Ip is the primary current. Let us assume both the column response C(r) and specimen response S(r) to be two-dimensional distributions of independent normal random variables. The normal distribution of BSE and SE2 (i.e., the shape of S(r)) was proved by Hasselbach and Rieke (1982) above 20 keV so at lower energies it can be assumed only as a rough
SCANNING LEEM
375
approximation and the same holds for the shape of C(r). One way of assessing the pixel size is to take the RMS distance of the emitted electron, dRms, which can be calculated for the axially symmetric case as
dRMS - - 2
[So-r2Ir(r) dr
/s0-1 ''' IT(r) dr
After substituting from Equation (45) Gaussians for both C(r) and S(r), we get dRMS
and
taking
(46)
two-dimensional
-- [8 -I- 0(1 -t- ,BS)l-'/218d 2 -I- 0(1 -I- flS)(d 2 -t- d2)] 1/2
(47)
where dp is the spotsize and ds is the RMS width of the specimen response. Equation (47) was then used for the estimation of the best achievable values of dRMS at low energies. The emission yields were calculated from the approximate relations reviewed above and the primary spotsize was assumed both for a standard SEM and for the CL-equipped one. The RMS specimen response ds was determined by M C simulations using software described by Czyzewski and Joy (1989) with the result
ds ~ CP-1E 1"75
(48)
where C - 9 x 10-ll kg m -2 eV-1. With the approximations described above, the pixel size dRMS exhibits a minimum (see Figure 27) enabling one to define the optimum imaging conditions for a particular specimen when the total electron emission is detected, as it is in most versions of SLEEM. Hence
"t"
,
,
'
'
I
'
'
!
. . . .
I
'
/ ~
//
10 2
//
TEG
nm +__
10 ~
f
f
f
f
f
~s
10 0 .
.
.
.
.
|
10 a
.
.
.
.
,
,
,
,I
104
Ep [eV]
FIGURE 27. Comparison of the primary spotsize ( - - ) with the total pixel size dgMs calculated for Cu (. . . . . ). The CL parameters were l = D = 5 mm and the summation rule (37) was used.
376
MOLLEROVA AND FRANK
optimum energies of the electron impact and ultimate values of dRMs were calculated for all three configurations indicated in Figure 27 and for the majority of chemical elements. The optimum energies move between 330 and 4530 eV while the ultimate resolutions were found as 5 to 13 times the nominal spotsize at 30 keV for both microscopes without CL and only 1.6 to 2 times for the CL-equipped model TEG SEM (Frank, 1996a). However, these data provide only broad guidance because of many simplifications made. The approach employing the specimen response function can be extended one step further, provided the SE emission is considered only (see Frank, 1996b). In the previous derivation we took the specimen to be fully homogeneous, with all yields constant with respect to r. Now we can progress to a specimen composed of a homogeneous substrate with a heterogeneous surface film or surface relief. Then, both r/and/~ in Equation (47) remain position independent but the emission distribution IsE (r) can be written as a convolution, Ise(r) = 6(r) | ise(r), with isE(r)/Ie = C(r) +
~[C(r) | S(r)]
(49)
which enables us to separate the imaged surface from the distribution of illumination by both PE and BSE. Because S(r) does not vary over the surface for a homogeneous substrate, we get the true specimen response function, which can be, for C(r) and S(r) approximated by Gaussians, written as ' R F -- G2(crp, r) + j3~(Z)G2 [ ( 4 + cr2)1/2, r]
(50)
where G2(ff, r)=(2rc)-lcr-2exp(-r2/2~2) is the two-dimensional Gaussian function. Equation (50) opens possibilities of using any acknowledged resolution criterion, like the Rayleigh one or those based on a certain encircled portion of signal, in addition to the evaluation via statistical moments that was performed before. In Figure 28 the real resolutions for C, Cu, and Au are compared for the Rayleigh criterion and the pixel size defined by 80 and 90% of the encircled signal. Obviously, the appearance of the resolution minimum, as in Figure 27, is connected with criteria oriented to the total signal (like dRMs) or to its major portion (like d9o). In the dR curves the minimum is not present at all and the dnn curves exhibit the minimum (connected with a significant influence of SE2) only for very high percentage nn. Already at nn = 80% the minimum disappears for the lightest element and at lower nn it is also not found. The above analysis showed that the real resolution has to be assessed by means of criteria oriented onto the central peak of the total response
SCANNING LEEM
101 ......
377
101 "in-;; - '/// I/. ... :". ..
......
~d~176
. . . . .
nm
nm
dR(C)
"
-0:c o,
dRo
- - - d.(Cu) ~ . -
d.(Au)
10 0
10 0 ~ .
. .|
. . . . . .
,
103
. . . .
!
,
.
.
. 1
104 Ep [eV]
"
.
.
,
i0 3
(a)
.
.
.
.
!
.
.
10 4 Ep [eV]
(b)
FIGURE 28. (a) Resolution dR calculated from IRF according to Equation (50) when the Rayleigh criterion is used (i.e., a drop of IRF to 36.74% of the maximum; see Born and Wolf, 1975) for three elements, with dRo representing the first term in Equation (50) only; (b) resolution dnn for nn= 80 and 90% of the signal encircled within the diameter defining the resolution, again with d,,,,ofor the first term in Equation (50). Parameters of the model FEG SEM and Equation (37) were used. function, i.e., criteria based on a certain decrease of I R F with respect to its maximum or on some encircled signal. These criteria show only a small extension of the pixel size with respect to the primary spotsize, as exemplified in Figure 28. On the contrary, the statistical moments of the signal distribution in the specimen plane overestimate the influence of species having diffused to great distances so that fully unrealistic figures appear at higher energies (see Figure 27). This indicates that even at low energies the conventional resolution tests can be used provided their evaluation respects the above-mentioned circumstances.
E. Spurious Effects The spurious effects influencing parameters of the electron probe in SEM are listed in Section II.C. Some of them are connected with the Coulomb forces acting between electrons moving within the beam so that the intensity of effects depends on the beam energy. The main phenomena include probe size broadening owing to stochastic e-e interactions, broadening of the energy spread (the Boersch effect), and defocus or probe shift caused by the overall space charge. The probe broadening caused by stochastic interactions was studied by Spehr (1985). He found the spotsize enlargement proportional to the normalized beam current
~: -- ~
I(Eo)
~-~
3/2
(51)
378
MULLEROVA AND FRANK
where I is the beam current, ot is the angle of beam convergence, I0 = 3.41 x 104 A, and E0 is the rest energy of an electron. This E -3/2 dependence is further enhanced by another factor that increases with decreasing energy with progressively varying slope and cannot be characterized by a simple proportion, but for short slow beams it approximately behaves as In 2 (const x E - l ) . Naturally, the final crossover at the specimen surface is the most critical one because the energy is lowest there. In cathode lenses, the beam aperture grows toward the specimen surface a s O/2(3( E -1 SO that altogether we get the probe-broadening rate somewhere around E -1. Mankos and Adler (2002) explored the problem of stochastic interactions for the cathode lens configurations. Using precise tracing of particle bunches through calculated electric and magnetic fields for both electrostatic and compound lenses with non-overlapping retarding and focusing parts, they obtained the "blur" values for wide ranges of the beam current and current density. Being oriented to direct imaging in the PEEM mode, their data range is shifted to larger currents and lower densities than those corresponding to the SLEEM situation. We can extrapolate their data to our case, the probe current of 5 pA and the spotsize of 10 nm at lowest energies, i.e., to the current density 5 x 103 mA cm -2, and obtain a broadening of about 1 to 2 nm. Otherwise, a linear increase in the blur with decreasing E~, was found. As regards the increase in the energy spread owing to e-e interactions, we already mentioned the fundamental work of Rose and Spehr (1980). For the stigmatic focus they calculated the extra energy spread to be (AE/E)= 2rcK (see Equation (51)) for low currents, so that AE~I1/2E1/4. This result is independent of the beam aperture ot provided ~c<< 1 and ol << 1-2E/Eo. The second condition is easily satisfied and for a beam current of 5 pA and aperture of 1 mrad, we get ~: ~ 2 x 10 -2 at 1 eV while for larger energies it further decreases as E -3/2. Thus, the Boersch effect is not enhanced at low energies. The average space charge within the whole beam acts as a divergent lens causing some defocus of the primary spot. Spehr (1985) showed that for a constant current density across the beam and ~c< 10 -2, refocusing of the appropriate lens enables the spot broadening to be corrected with negligible residual effect. For an electron beam with Gaussian cross-section, a contribution to the spherical aberration is generated too, with the corresponding confusion disc that, again for low currents, has a diameter de-e= 1.1~:D0, where Do is the diameter of the beam-limiting diaphragm. Nevertheless, at the same time it is claimed that this deviation can also be corrected by readjusting the lens excitations. The proportionality to ~c, i.e., to E -3/2, requires the effect to be listed here although there are no reports
SCANNING LEEM
379
about its practical demonstration so that successful correction via fine focusing can be believed. Important spurious effects in SEM are caused by the penetration of external electromagnetic waves into the column. These phenomena were reviewed by Frank and MfillerovS. (1999) and found negligible except the beam deflection 3y caused by a radial magnetic field Br, which amounts to 6y -- eBr (2Elm3) 1/2z"2 with ~ as the time of flight across the region exposed to the magnetic field. The beam trajectory inside magnetic lenses is shielded by magnetic circuits against the spurious fields relatively well so that the most exposed part is the trajectory along the working distance between the lower polepiece of the objective lens and the specimen. If this region is traversed by slow electrons at energy E, the time of flight is (1 + ~/k)/2 times longer than when electrons are decelerated to E from the primary energy Ee along the same trajectory. This means that the beam deflection is reduced (1 + ~/k)2/4 times, i.e., for example 266 • for k--1000. From this point of view, insertion of the cathode lens below the magnetic objective lens represents the optimum solution. Finally let us recall the problem of mechanical vibrations. This issue is common to all types of SEM and its impact simply depends on demagnification of the gun crossover. The most sensitive component to any vibrations is the cathode itself but in TEG SEM its movements are demagnified 103 to 104 times together with the crossover and become negligible. However, for FEG operated at room temperature the necessary demagnification remains of the order of units, so serious problems arise unless the device is carefully insulated from vibration sources. This problem is not specific to the SLEEM mode.
F. Testing the Resolution We have already mentioned that, even at low energies, the conventional tests of resolution, made with a specimen containing small particles of a heavy metal on a low-atomic-number substrate (most often gold on carbon), can be used provided their evaluation respects the signal composition of SE1, SE2, and BSE. For psychological reasons, it is desirable to extract from these tests numbers that approach very closely the calculated spotsize without any enlargement owing to diffusion inside the specimen. This means the tests should be performed solely upon the SE1 signal. In previous sections we showed that in the low-energy range where the lateral spread of SE2 and BSE emission shrinks and approaches that of SE1, progressively enhanced fraction of SE release takes place within )~esc and hence the SE1 signal relatively grows. It is reasonable to suppress the
380
MI21LLEROVA AND FRANK
distribution tail that appears in the edge width measurement by taking the thresholds far enough from the signal levels on adjacent facets; the proved algorithm is to measure between levels of 25 and 75% of the signal rise. Reimer (1998) used MC simulations to model the resolution test for emission distributions of all signals and also their integrals on one side of a moving straight edge and verified applicability of the 25/75 scheme. As we will discuss in the next section, the SE and BSE signals are detected together in the SLEEM mode and therefore extension of the lateral distribution of the total signal with respect to that of SE1 becomes even more probable. Nevertheless, practical experience showed that also here the 25/75 rule is suitable (see Figure 30). Another crucial circumstance, not taken into account with a conventional SEM, is the necessity of using a specimen that preserves a sufficient contrast throughout the full energy scale. It is believed that a difference in atomic numbers as large as that between Au and C should secure this. However, we see in Figures 13 and 16 that the signal yields already change their mutual relations drastically above 250 eV; other published data confirm this down to even lower energies, as Schmid et al. (1983) showed for eBSE. The contrast behavior of the standard Au/C specimen was verified in two instruments equipped with the same SLEEM detector and CL assembly described below. The microscopes differed mainly in the vacuum conditions; one had the usual medium vacuum (MV) of the order of 10 -4 Pa and the other used clean UHV at about 2 x 10-8 Pa. As shown in Figure 29, at 320 eV for both devices the Au/C contrast is substantially less than that at 3 keV but at 20 eV for the MV instrument the contrast fully disappears, while in UHV it is inverted and quite high. Surface contaminant layers being less transparent at 20 eV under worse vacuum might cause the difference but as yet the interpretation is not fully clear (see Mfillerovfi and Frank, 2003). Nevertheless, fine cracks are still apparent at the surface, the contrast of which is obviously due to enhanced electron absorption in deep cavities, and an appreciable signal rise at edges can be observed. Figure 30 shows a linescan across such an edge, taken at an electron energy of 10 eV, which demonstrates a resolution of 9.3 nm, to the authors' knowledge the best one achieved yet (Mfillerovfi and Frank, 2002). This value corresponds to the objective lens aberrations C s = 3 3 mm, C c - - 1 5 mm, published by Takashima (1994) for the working distance (WD) of 6.5 mm, and to W D = 8 mm used by us, which is larger than that appropriate for the guaranteed instrument resolution (1 nm at 15 keV). As regards the UHV SLEEM, the same measurement gave 11.5 nm at 10 keV and 26 nm at 10 eV.
SCANNING LEEM
381
FIGURE 29. Micrographs of the standard resolution-testing specimen with Au particles on a carbon substrate, taken (from the top) at 3020, 320, and 20 eV. Left column: dedicated UHV SLEEM of ISI Brno, right column: JEOL 6700F adapted for SLEEM. The width of the field of view is 100 ~tm (top left) and 200 lam (top right). (Reprinted with permission from Mtillerov/t and Frank, 2003.)
VI. DETECTION AND SPECIMEN-RELATED ISSUES
This review concentrates on SEM modes employing primary beam retardation close to the specimen. In the majority of instances the retarding field is also traversed by the signal electrons in the opposite direction so that these are accelerated and, if the field has its axial component strongly
382
MOLLEROV]k AND FRANK J
,
,
,
,
.
.
.
.
,
.
.
.
.
i
.
.
.
.
,
.
.
.
.
,
.
.
75%
.
.
.
.
i
.
.
.
.
i
.
.
.
100
.
i
.
.
.
.
.
,
.
.
.
.
,
.
.
.
.
.
.
.
i
.
.
.
.
,
,
,
,
~ A
.........
0
.
i
.
.
.
200
.....
.
i
.
.
.
.
\
i
1
.
.
.
i
300
.
i
i
i
i
l
i
.
.
.
400 nm
FIGURE30. Linescan acrossanedgein a micrograph ofthe Au/C specimen, taken a t a n energy of 10 eV (JEOL 6700F adapted ~ r the SLEEM method), with the edge width indicated.
prevailing, also collimated toward the axis. In the cathode lens configurations the specimen itself becomes one electrode of the electron optical system. These facts have a decisive impact on the choice of detection principles to be used. First of all, the classical Everhart-Thornley detector, extracting slow SE by a lateral electric field, cannot be used because the emitted electrons are being accelerated along the axis and also because the slow primary beam could be undesirably affected. Hence the objective lens with its focusing and retarding parts has to be considered together with the detector. Further, owing to acceleration of signal electrons, the crucial difference between typical SE and BSE energies is shifted so that usually both appear in the same order of magnitude. Then, separate detection of SE and BSE via conventional methods is not efficient any more and novel detection principles are needed. Finally, the specimen surface parameters, the roughness in particular, have to be considered for the cathode lens assemblies.
A. Detection Strategies In previous sections we frequently compared the properties of the immersion objective lens (IOL) in its general form with the particular case for w =0, in which the retarding part is called the cathode lens. It is worth continuing this also here: as demonstrated in Figure 31, the formation of the "signal beam" is significantly different in these cases.
SCANNING LEEM
383
FIGURE 31. Trajectories of electrons in the electrostatic immersion lens (a) and cathode lens (b); the potential difference within the lens is 10 kV; energies of electron emission are 5 eV (bottom half of the bundles) and 200 eV. The simulation was made using the SIMION 3D package (Dahl, 1995). (Reprinted with permission from Miillerov~tand Frank, 1999.)
For the IOL in the low-energy range, a non-negligible part of BSE impinge on the first electrode and can be detected in this plane while the SE emission is concentrated to a bundle that is focused into some crossover and then again spreads. This formation of an image of the emitting pixel is further supported by the focusing part of the IOL. Thus, the SE beam can be acquired even around the axis in a suitable plane above the IOL with a detector type normally used for BSE. The arrangement (see Figure 22) is then similar to the so-called "upper" SE detector utilized for acquisition of the SE beam from a specimen immersed in the magnetic field of the objective lens, which collimates the SE emission toward flux lines of the field (see Kruit and Lenc, 1992). Here the SE beam is already accelerated so that its detection is easier. The upper SE detector is usually situated above the deflection stage so that its action also influences the trajectories of signal electrons and a general issue here is to minimize or avoid escape of signal through the detector bore. We will discuss this problem further in the next sections (see Figures 40 and 46). If a CL is used (Figure 3 l(b)), the signal electrons are collimated to a diverging beam the width of which depends on emission energy and CL parameters. If we solve the classical equation of motion for an electron emitted with initial energy Ee under an angle | with respect to the surface normal into the CL field within which it is accelerated to energy E,,, we get for its radial coordinate ra at the end of field, i.e., in the anode plane, 2l sin|
[t e-sin2 t --COS] 1/2
384
MLTLLEROVA AND FRANK
where ke= Ep/Ee is the immersion ratio for the emitted electron, defined analogously to k. The entire emitted bundle for | is then concentrated into the spot of radius 21
ra'max = The
angle
of passage through
--l~/K/Z e----~ "
the
anode
(53)
plane,
O/a,
is given as
sinota=ke-1/2sin| so that the angular aperture of the bundle is Ota,max=arcsin (ke-1/2). W h e n drawing a ray backward from the anode plane, we find it crossing the optic axis, according to its emission angle, between l and l(kl/2-1)/(kl/2+ 1) behind the cathode, with the latter position corresponding to the paraxial ray. This virtual source is further imaged by the aperture lens in the anode plane and by the focusing part of the IOL. For secondary electrons with characteristic energy 3 eV (see Section IV.D) and for typical values of l = 7 mm and Ep = 15 keV, we get ra,max--0.2 mm and Ola,max~- 14 mrad. The beam of backscattered electrons is formed according to the BSE energy, which is dependent on the landing energy of the primary beam, but at very low energies similar figures are obtained to those for SE. Obviously, the detection made below the focusing lens has to be extended up to the close vicinity of the optic axis or again the throughthe-lens principle has to be incorporated. The previous simple considerations indicate a general problem: we have a narrow signal beam along the axis, escaping at least partially the detection through the central bore left for the primary beam. The signal losses can be reduced if the signal beam can be again broadened within a suitably arranged electric field as is done in the EDOL-type lens already mentioned; we will return to this arrangement in the next section. The issue can be fully solved via deflection by means of crossed electric and magnetic fields, i.e., by a so-called Wien filter or E x B filter (see Figure 32). The electric and magnetic forces subtract for the primary beam direction, but for the opposite signal beam direction they add and cause its deflection toward the detector. The Wien condition for equality of electric and magnetic forces can be easily fulfilled for the homogeneous parts of the fields but it is more difficult to satisfy for the spurious fields at the margins of electrodes/polepieces. In addition, any spread in electron velocities causes beam dispersion. This is why two identical but oppositely oriented filters are often incorporated so that the primary beam passes both and any undesired modifications are mutually compensated while the signal beam escapes between the filters (see Figure 46). In order to further minimize any influence on the primary beam, the Wien filters can be made
SCANNING LEEM
385
:Z
aaee 'or ~FapFE
.
.', ........
F
........
FIGURE 32. Principle of the beam deflector employing crossed electric and magnetic fields.
weak, just sufficient to deflect the signal beam to where it can enter some other electric field, not penetrating to the optic axis, that extracts it strongly towards the detector; for example, see Figure 33 and the same principle is shown in Figure 46. Various modifications of detector assemblies containing Wien filters have appeared in the literature since the 1980s (e.g., Schmid and Brunner, 1986; Brunner and Schmid, 1987; Reimer and Kissens, 1994; McKernan, 1998). Zach and Rose (1986) studied the influence on the primary beam of filter aberrations and proposed using higher order than dipole fields. A detailed study of the filter properties, including fringing fields, was presented by Kato and Tsuno (1990). A significant effort has also been invested in shifting the range of efficient operation of BSE detectors down to lower energies, i.e., in breaking as much as possible the traditional threshold at 2 to 3 keV. The amendments include both technological improvements concerning the preparation of scintillator surfaces and the introduction of extraction fields in such a way that secondary electrons are still not incorporated. Important studies include those of, for example, Autrata and Hejna (1991), Autrata et al. (1992), Hejna (1994), Autrata and Schauer (1994) and Hejna (1998). New detector principles have emerged that employ sophisticated arrangements of electric fields, created by electrodes situated within the magnetic lens bore and gap, and permitting a wide range of manipulations with the emitted electrons and extension of the scope of operation modes of the upper SE detector. These operation modes include collimation of the SE beam for enhanced detection efficiency, reflection of a portion
386
MULLEROVA AND FRANK
- - - - - - - - - - x(z) .... y(z)
/f,
j"l
.........
!
/
prima~;r
iI i
~ ~ ,~
9
L(L(L~
*
.......
~es '
"~
[magnetic .... i saddlecoils 1] / magn"circuit / ,
9
.
I
|
9
,
9
,
.
.
1 cm
~ ,
I
9
I! I
1///
upperstage 9
'
i///
9
|
|
i
.
.
.
.
I magnetic I saddlecoils l] magn"circuit ]
lowerstage
' i
,
,
,
,
I_l
I
i
i
,
,
,
i
I
,
9
9
,
i
,
,
,
,
FIGURE 33. Scheme of the double Wien filter with intermediate electrostatic mirror for deflection of the signal beam in an SEM. The bundle of SE trajectories is shown for the emission energy of 4 eV and emission angles within + 70~ Ub = - 10 kV. (Reprinted with permission from Pejchl et al., 1994.)
of the SE in order to achieve the charge balance at a nonconductive surface without charging, and, in combination with a moderate specimen bias, conversion of accelerated SE, impacting a converter surface, to tertiary electrons that are detected normally. In this way, good-quality micrographs were obtained down to 100 eV (Kazumori, 2002). An analogous configuration of electrodes, combined with the E • B filter, enables one to control the content of SE and BSE in their mixture detected by a single (upper) detector. In this configuration, BSE are converted to SE and biases of the electrodes can discriminate between SE from the specimen and those from the converter surface. These combinations with the crossed E • B fields appeared for the first time in the early 1990s (see Sato et al., 1993). Inevitably, arrangements of all electrodes are being published only schematically because details are considered confidential. Nevertheless, the CAD systems available do enable one to tailor the above-specimen fields in various ways and to optimize the detection efficiency for individual portions of the energy and angular distributions of total electron emission.
SCANNING LEEM
387
B. Detectors
In the previous section we listed the possible approaches to detection of electrons in systems with retarding field elements. Now we will describe several actual configurations. For IOL setups, i.e., with the retarding field not directly applied to the specimen, the variety of detector assemblies is very broad. For SE detection, they mostly rely upon the through-the-lens principle and detect SE either with a coaxial scintillator-type detector or deflect them by an E x B element toward a side-attached detector similar to the ET type. As regards BSE detection, conventional assemblies below the IOL polepiece are utilized but novel approaches have also appeared that include conversion of BSE to SE and detection of a controllable mixture of SE and BSE as mentioned above. Let us recall here the simple EDOL arrangement published by Zach and Rose (1988) (see Figure 34(a)), in which an accelerating electrostatic lens is employed and designed so that the conical electrodes generate significant radial components of the field. Within the first accelerating part of the lens, the SE emission is collimated to a beam while in the decelerating part the beam is, owing to radial forces, appropriately broadened so that it hits the annular detector with a reasonably large central bore. In a configuration according to Figure 34(b), the decelerating part of an electrostatic lens is similarly utilized to broaden the beam but here the lens is of the decelerating type and hence its first part is employed for this purpose. A further difference consists in using the conical electrode as the electron converter transforming accelerated signal electrons to tertiary electrons that are directed by the radial field toward a microchannel plate (MCP)-based detection assembly (Frank et al., 2000a). In this setup, the collection efficiency for 10 eV signal electrons, i.e., the probability of their impact on the converter surface, was calculated to exceed 98% and, after conversion and passing the MCP, 35% of emitted electrons still create signal impulses. A setup on this principle, an electrostatic detector lens (EDL), can be more widely utilized as it enables one to introduce a segmented or even twodimensional collector below the MCP and to acquire data about the angular distribution of emission. For completeness, let us also recall the MEDOL configuration (Figure 22) in which the signal beam is projected onto the detector by the combined action of both components of the compound lens. Now we will specifically deal with detection in systems that employ a cathode lens, particularly those based on adaptation of a conventional SEM. The authors' first experimental arrangement contained the detector assembly shown in Figure 35(a) (Mfillerov~t and Frank, 1993) in which, on the surfaces of the diaphragm and lower polepiece of the objective lens (OL),
388
MOLLEROV,~t AND FRANK
Conv SE traje
~
0 v (8 keV)
annular detector /
7 kV (15 keV)
CPI
7.5 kV (500 eV)
CPO Coil
_
Sp
, / / ~ specimen --- 20 mm --~
(a)
(b)
FIGURE 34. (a) Scheme of the EDOL arrangement with an accelerating lens that broadens the signal beam inside its decelerating second part (electrode potentials are shown together with electron energy in parentheses). (Reprinted with permission from Zach and Rose, 1988.) (b) Similar principle combined with a converter of accelerated signal electrons into tertiary electrons detected by a multichannel-plate-based assembly (L, lens; Conv, convertor; CPI and CPO, input and output of MCP, respectively, Coll, collector; A, anode; Sp, specimen). (Reprinted with permission from Frank et al., 2000a.)
the accelerated signal electrons are converted to tertiary electrons and these are attracted to a conventional ET detector with the front grid removed in order to allow the scintillator field to penetrate towards the axis, as shown in Figure 35(b). The advantages of this type include very low price and easy realization but the drawback is the quite large working distance that is necessary. In fact, the same arrangement was introduced by manufacturers in the form of the upper detector with converter (see above), but for an easy adaptation in users' laboratories the space above the SEM objective lens was, of course, not accessible. Another successful design employed the single-polepiece magnetic lens situated below the specimen (see Figure 26(b)), now completed with the anode of a CL and a BSE detector with a YAG crystal; the scheme of the assembly is shown in Figure 36. In this setup, a micrograph with a resolution of 80 nm at 0.5 eV electron energy was obtained for the first time (Mfillerovfi and Lenc, 1992b). This type is hardly suitable for adaptation of classical SEM instruments but was used, for example in a specialized lowenergy SEM for inspection of semiconductor structures at a landing energy of 800 eV and a primary energy of 20 keV (Meisburger et al., 1992). The most successful arrangement to date is shown in Figure 37. A crucial component is the YAG:Ce 3+ single-crystal scintillator disc with small central bore of depth and diameter 300 pm, side-attached to a light guide
SCANNING LEEM
~
oPOlepiece of OL
~~176
anode ~
assembly
~
~
~
~t~ " Y ' ~
.... ~
I
' i
,.=.~I
]I ' ' ,
/
/
~
/
/
i L. . . . . . . . . . . /
OL
ETdetector
I I-t[-l\,c m .............. t l l l a t o r -A--
,n
0.1V
~____a~:~ .... 9 ~
Ub _ =__..a
~"
389
.....
,t
1V lOV lOOV
lOOOYl
.... ~ ~ \ ~ _ _ _ _ J anode of CL
§ ~+lOkV
\ specimen
J I
sc~tillator
~'
insulator
FIGURE 35. Configuration of the SLEEM mode detector utilizing conversion of accelerated signal electrons on surfaces of the diaphragm and lower polepiece of an OL, and extraction of tertiary electrons toward a conventional ET detector (left); equipotential surfaces within the assembly when the front grid of the ET detector is removed (right). (Reprinted with permission from Frank and Mfillerovfi, 1999.)
OL p o l e ~
light-guide
/~
~ ~
9 9 elmag. shielding
in-lens deflection coils anode of CL specimen
i>/' single polepiece lens
[,,
9
p
I ~
FIGURE 36. A combination of the cathode lens with a single-polepiece lens situated below the specimen.
390
MOLLEROVA AND FRANK
~JE PRIMARY
LECTRONS
~E
DIAPHRAGM ANODE
DETECTOR CATHODE/ LENS
Ub
SPECIMEN
INSULATOR
FIGURE 37. The CL/detector assembly with a YAG:Ce 3+ single-crystal scintillator. (Reprinted with permission from Frank and Mfillerovfi, 1999.)
made of organic glass (for standard vacuum applications) or of quartz (for bakeable UHV instruments). The bore size was tuned to some balance between reasonable dimensions of the field of view and successful acquisition of very-low-energy electrons collimated towards the close vicinity of the axis. As shown in Figure 38, for one typical set of dimensions (used in the experiment described in Section VIII.E) and for normal impact of PE, signal electrons are detected above 0.5 eV of emission energy. This configuration is similar to the so-called Autrata-type BSE detector (Autrata, 1989) but important differences are the much smaller central bore and the related necessity for fine adjustment of the crystal position in all three axes. Fortunately, this adjustment is decisively facilitated by the fact that the upper crystal surface is also active so that the detector bore is directly observed on the SEM screen (see Section VII.C). The bore shape with a 45 ~ sink is dictated by several issues that include requirements of the boring technology, feasibility of a conductive coating of the inner bore wall, and an advantageous axial field distribution. It is obvious from Equation (42) that one term in the relation for Cs, namely aberration of the anode field, is inversely proportional to the bore diameter D and hence D should not be made too small.
SCANNING LEEM
(~)m [deg] 80
I
.
.
.
.
I
"
'
'
'
391
'
I
'
"
'
"
60 40 20 i
10 "1
i
I
i
,
,
10 o
.
I
101 Ee[eV]
102
FIGURE 38. The maximum emission angle, l~)m, of an electron with the emission energy Ee for which the electron still escapes through the central bore. Solid line: data calculated from Equation (52) for ra=0.15 mm, l = 11 mm, E~,= 10 keV; squares: exact values obtained via trajectory simulations using a software described by Lencovfi and Wisselink (1990). (Reprinted with permission from Frank et al., 1999.).
'7,
j
.... ; .......
E2
0
2
4
z [mm]
6
8
10
FIGURE 39. Derivative O~/Oz of the axial potential distribution (I,(z) for the three anode shapes outlined in the inset (calculated using software described by Lencovfi and Wisselink, 1990).
The shape shown in Figure 37 produces the axial potential distribution that resembles more closely the distribution corresponding to the outer diameter of the sink than that of the inner one (Zoba6ov/t et al., 2003); see Figure 39.
392
MOLLEROVA AND F R A N K
upper SE detector
scanning
coils
! V//////'/////A
OL
,i__~'W~N~ ~] ] ~////////~ a n o d e specimen I i
FIGURE 40. Scheme of trajectories of primary and signal electrons in a CL-equipped SEM with an upper detector.
With regard to adaptations of commercial SEMs to the SLEEM method, we should also mention an alternative employment of the upper SE detector, either in a coaxial arrangement or side-attached one with the electron converter, when it is combined with a CL operated between the specimen and the lower polepiece of the OL. Here we gain the space required for the detector as in Figure 37, so that a shorter working distance can be attained. In Figure 40, a sketch of electron trajectories is shown for the case when none of the above-mentioned additional electric fields for manipulation with signal electrons is considered. All previously described setups are intended for adaptation of conventional SEMs that naturally have their full columns at the ground potential and hence any retarding field can be created only via a specimen bias. This can impose serious difficulties particularly for instruments equipped with an air-lock for insertion of a specimen cartridge. But in any case the specimen biasing loads the routine operation with extra tasks and checks. It is much more convenient to use the booster principle with a positively biased central tube that creates the necessary retarding field even toward the specimen at ground potential--the next section will address these questions. Here again we should recall the family of IC testers in which CL/detector assemblies are increasingly used and designed subject to an extra requirement that is not so important for other SEM applications, namely
SCANNING LEEM
393
that the beam current be as high as possible in order to achieve a high throughput in the productions checks (see Section VII.B).
C. Signal Composition Within the CL field the whole energy spectrum of emitted electrons, outlined in Figure 11, is accelerated by the potential difference between specimen and anode. For larger CL fields, the energies of the SE and BSE are of the same order of magnitude and no type of detector can efficiently separate them unless a true energy filter is incorporated. The particular composition of the signal mixture depends on parameters of the fields and on the geometry and here we can only show one typical example. Let us consider the CL/detector assembly according to Figure 37 with a YAG:Ce 3+ crystal for which Autrata and Schauer (1998) published the detection quantum efficiency (DQE), defined as the squared ratio of the signal-to-noise ratios (SNR) at the scintillator input and output. For a cosine distribution of both SE and BSE emissions, the portion of electrons hitting the scintillator (or the collection efficiency) is simply
P = IDET/I = sin2~max -- sin2Omin
(54)
where Oma x and (~)min correspond to the marginal rays incident onto the scintillator, which can be determined from Equation (52). Figure 41 shows P and DQE for both SE and BSE, plotted with respect to the landing energy of the PE together with the detection weight
WBSE/SE
--
PeSE DQEBsE PSE DQEsE "
(55)
This obviously favors BSE in a ratio between 5:3 and 4:3. Since the SE yield usually surpasses the BSE one, the signal mixture, governed by the weight WesE/SE, represents a more or less balanced combination of both components. The graph in Figure 41 depends on particular values of three parameters, Ep, D/1, and Do/l (Do being the outer scintillator diameter), but also for other reasonable combinations of these factors similar results for WeSE/SE are obtained. With below-the-lens detectors the BSE/SE ratio cannot be efficiently controlled and generally a sum of both signals is obtained. On the contrary, setups employing the upper detector open possibilities for controlling the signal ratio at least down to about 200 eV where SE and BSE cease to be
394
M[JLLEROV]i '
'
i
9
9
:
1
:
......... ~"
..'~" _~
~
9
FRANK
i ,
-#.
9
:
,
'
:
i
9
r
~
i
o__,_~___o . . . . .
...................
',
_._P~ ~ "~z ..... DnE "',
\/
-,.K,
--~ , ..... r
BSE
~
101
-"
..~
.-. .~. .. ~ .t . . > ~ . .,,
. . . .
9
,~,_-~, . . . . . . . 9 . . . . . . ,
',. . . . . . . . . . . . . . . . . .
. . . . . . .
w-
PSE
":'I-.-~
,
0
9
,
~. ~:._ ~ - b - - 4 - ~ . . . . . . . . r
0.5
AND
"
%
. . . . . . . .
10 2 emission energy,
10 3
10 4
Ee[eV]
FIGURE41. Collection efficiencyP for SE emitted at mean energy of 3 eV, for BSE emitted at 75% of the landing energy of PE (above 50 eV), and for eBSE below 50 eV, calculated for the assembly shown in Figure 37 with a crystal outer diameter 10 mm and bore diameter 0.3 mm and field length l= 7 mm, together with the DQE values corresponding to the various impact energies and with the weight W~SF4SEaccording to Equation (55).
distinguishable even in the energy spectrum of emission--see simulation results of K u h r and Fitting (1998).
D. Specimen Surface One important characteristic of an IOL is the magnitude of the electric field penetrating toward the specimen surface. For the CL as the extreme case, the surface field is the m a x i m u m retarding field used, while IOL arrangements with a nonzero working distance w, i.e., with the specimen electrically connected to the first electrode, are usually regarded as situating the specimen in a field-free space. Let us assess the field penetration outwards of the retarding lens for a simple case of flat electrodes of the same thickness t and identical bore diameter D, situated at distances w and w + l from the specimen, as in Figure 21. For three particular IOL geometries we show in Figure 42 the ratio of the surface axial field to the m a x i m u m axial field within the lens plotted versus w/l, together with the immersion ratio k for which the IOL alone focuses the beam onto the specimen surface. We see that for very low energies, i.e., say for k _> 500, the surface field does not drop below 10% of E z , m a x . Nevertheless, if a magnetic lens contributes to the probe focusing, the working distance further shortens. If both lenses are of an equal optical strength, the surface field is E z - 0.5Ez, max.
SCANNING LEEM
I
,
..~ 10 2
,
:
,
~
,
~
"
,
,
~,
~,
,
-.
' ,
! ,
~ :
~.
~
395
~' ~
,
,
,
,
",,.._b",~.a ~'--.~
"--.
',
:
01
10 0
10 -1 0
0.3
0.6
0.9
1.2
working distance, w/I FIGURE42. The axial field strength on the specimen surface referred to the maximumfield strength within an IOL, and the immersion ratio k for focusing the probe by the electrostatic lens only, plotted for three configurations of the IOL with flat thin electrodes: (a) D = l, t = 0; (b) D = l, t--0.1 l; (c) D = l/2, t--0.1 l (for symbols see text). Obviously, the field penetration has to be taken into account even for an IOL with a nonzero working distance. In order to improve the situation, the lens electrodes have to be shaped and their bores tuned to create an axial potential distribution falling as sharply as possible in the close vicinity of the specimen. For this task powerful simulation software packages are available; the optimization procedures were studied by Preikszas and Rose (1995). We will now address the specimen surface roughness. While no problems are expected and appear with an IOL, it has been repeatedly argued that a CL is unsuitable because the specimen surface has to be very smooth if not polished like that of an electrode. Practical experience shows that the real demands are not so strict albeit application of the method is without any doubts restricted to observation of flat specimens. Naturally, the m a x i m u m applicable field between specimen and anode is restricted by the danger of a possible discharge that increases with the specimen roughness. Also the imaging process alone requires that the CL field should be homogeneous up to the very specimen, which can be so only for smooth surfaces. Tolerable roughness depends on shapes of protrusions and depressions and on the field strength. Any radial forces, connected with "waving" of equipotential surfaces above the surface relief, shift or smear the primary probe and locally deteriorate the image. Nevertheless, the above-specimen equipotentials do not simply copy the proper surface but depend also on the distribution of surface dipoles and any trapped charges.
396
MI21LLEROVA AND FRANK
FIGURE 43. Si (100) substrate with heterogeneously etched trenches of both width and depth 3 lam, with some traces of Cu decoration, imaged (from the left) at 5 keV, 250 eV, and 1 eV; primary beam energy= 10 keV, CL field -- 1.5 kV mm-1, width of the field of view= 20 ~tm. To the authors' knowledge, no study focusing on this issue has been published as yet. In Figure 43 we see one practical example of a specimen with known shape and dimensions of surface relief features and can verify that even in the 1 eV micrograph no traces of local deterioration at the trench edge are apparent. Other similar experiments also resulted in the conclusion that a surface relief up to a p - p height of a few ~tm could be tolerated for the SLEEM mode at moderate CL field strengths not exceeding 2 to 3 kV mm -1. Otherwise, in Figure 43 we can also notice a strong shortening of the depth of focus with decreasing electron energy. Restriction to a relief not exceeding a few gm is more or less in accordance with the depth of focus, which is here significantly shortened, owing to enlargement of the beam aperture within the CL by approximately ~/k times. Otherwise, limitation to the depth of focus is felt to be the most important disadvantage of the method and can be at least partly suppressed only at the cost of resolution, as indicated in Figure 25. Finally we recall one more of the traditional misgivings regarding the S L E E M / L E E M methods, namely that UHV conditions and atomic cleanliness of the surface are unavoidable because of extreme surface sensitivity. It is true that at around 50 eV of landing energy, where the minimum penetration depth of PE is achieved, the surface sensitivity is high and the image contrast is dominated by that of surface contaminants. However, above and particularly below this threshold the electron penetration grows steeply so that at a few eV it is comparable to that at tens of keV. This means that the method itself does not put any demands on the surface cleanliness but such demands might follow from phenomena to
SCANNING LEEM
397
be observed. For example, phenomena connected with surface crystallinity, reconstructions, phase transformations, etc., can take place solely on surfaces free of amorphous contaminants that might prevent atoms arranging according to the distribution of forces inherent in the crystal.
E. Specimen Tilt
When the specimen is not immersed in an electric field, normal conditions for the specimen tilting can be expected irrespectively of whether the retarding field is used or not. When only a weak field penetrates the anode bore toward the specimen, some balance has to be sought between the image shift and deterioration on one side and the tilt angle on the other side. In the CL any specimen tilt introduces a lateral field component that is not considered in the simple electron-optical theory outlined above. Small specimen tilt can be easily caused by imperfect fixing or sticking of the specimen to the holder so it is advantageous to have the specimen stage equipped with the double-tilt facility at least within a small range. However, it is also interesting to explore the limits of an intentional tilt introduced in order to get the primary beam incident under an angle. Let us now look at the consequences of a moderate tilt at an angle co. Having the anode of the CL in the plane z = 0 at potential 9 = 0 and the cathode at z = 1 and 9 = ~0, we get now the CL field, for the tilt made with respect to the y axis, modified to z
9 (x, z) - - ~ 0 l + x tanw"
(56)
A solution of the equations of electron motion in this field was presented by Frank et al. (1999). The lateral component of the CL field causes some shift A of the primary spot in the tilt direction. For small values of co this shift amounts to 2
a -5~
(v/-k - 1) 3
(k_l)2 ,
(57)
i.e., for very large k it tends to (2/3)co/. This magnitude of shift is quite significant so that when tilting the specimen intentionally, we have to do it in very small steps and to correct the position of the field of view in between. A further effect of the tilt is a unidirectional smearing of the primary spot owing to the lateral field created. In scanning devices, it is reasonable to express the image resolution via the number N of spotsizes filling the field of
398
MOLLEROV.dt AND FRANK
view and to compare this figure with the number of pixels acquired. Naturally, the optimum operation mode is achieved when these two numbers are equal. Normally, the spotsize and the size of the field of view are to a first approximation independent so that the optimum mode for a given number of pixels can be adjusted via the magnification. Nevertheless, imaging with some excess nonutilized information or with insufficient information density is also available for the magnification below or above the optimum, respectively. In other words, the number of spotsizes within the field of view is inversely proportional to magnification, and for any number of pixels acquired some optimum size of the field of view exists. In our case the beam inclination, generated by deflection coils in order to reach an off-axis pixel, plays its role in the spotsize deformation so that the optimum number of pixels N directly results from the configuration data as 3
N
TM
(7~/_~_ lO)otcW"
(58)
This number corresponds to the margin of the field of view while toward the optic axis the spotsize linearly diminishes toward its original dimension for no tilt. When taking typical values for the very-low-energy range, i.e., say k = 1000 and ore-2 mrad, and considering 1~ tilt, we get N = 407, i.e., a number on the edge of acceptability. An additional consequence of the tilt is the oblique impact of the primary beam, which is deflected by the lateral field component. Notice that this change in the impact angle is homogeneous within the field of view and has nothing in common with inclination due to beam rocking around the pivot point of the scanning system. For a certain deceleration, defined by a value of k, we get some tilt angle COmax for which the illumination becomes glancing: ~, (.Omax-
1 / 3 ( k - 1) k V
2
(59)
Independence of O)ma x on any other parameter offers an advantageous possibility of calibrating the true tilt scale according to the specimen bias causing a near-glancing impact easily recognized from long shadows of relief details. Otherwise, the impact angle can be assessed from Figure 44; this plot depends solely on Ee, which is here 10 keV. Obviously, the impact angle is, except in the near-glancing situation, well approximated by cok 1/2. Even very small tilts of tenths of a degree can at very low energies secure a full scale of impact angles, which is important for applications connected with the acquisition of the diffraction or energy-band contrasts.
SCANNING LEEM .
.
.
.
.
.
.
399
I
.
.
.
.
!
'
80
.'o
60
,
m 40
10 -1
10 0
101
10 2
landing energy, E [eV] FIGURE 44. Dependence of the beam impact angle on the landing energy for the specimen tilt angles shown (Ep= 10 keV); exact values are shown together with those approximated by o~k1/2. (Reprinted with permission from Frank et al., 1999.)
The above analysis showed that even with the CL the specimen can be tilted sufficiently to observe phenomena or features that require a tilt for this purpose. Moreover, the mechanical tilts necessary for large impact angles of the beam are only tolerably destructive as regards the image quality.
VII. INSTRUMENTS
A. Adaptation of Conventional SEMs As noted in the introduction, many attempts to design and build a SEM incorporating the retarding principle have been performed and the majority of them can be classified as adaptations of conventional instruments. Mfillerovfi and Lenc (1992a) reviewed the older works and we will not repeat here this literature survey. This section will discuss some recently applied approaches without aiming at a complete summary of relevant publications. It is obvious that in a conventional SEM the way of providing beam deceleration in front of the specimen is usually restricted to specimen biasing to a high negative potential. An additional electrode, placed above the specimen and electrically connected to it, enables one to arrange for a nonzero working distance of an IOL while without such an electrode we get
400
MULLEROV.~ AND FRANK
the CL. The latter alternative has proved itself successful in all groups of application tasks listed below in Section VIII and experience has been collected from adapting microscopes of all major manufacturers. After gaining preliminary experience with the configuration shown in Figure 35, the setup of Figure 37 was repeatedly installed because of its shorter working distance, easy alignment, and superior efficiency of the signal collection, albeit at a significantly higher price. Up to now, in all versions the YAG:Ce 3+ single-crystal scintillators were used with a thickness of 2 or 2.5 mm and outer diameter between 10 and 20 ram. The light-guide shape is partly dictated by the arrangement of the OL polepiece and of the x - y stage but otherwise some space exists for optimizing the shape with respect to the light transfer from scintillator to the side-attached light guide (see Schauer and Autrata, 1998). It is recommended to make the detector retractable so that the resulting restriction to the field of view is not preserved for other operation modes. It is sufficient to provide specimen insulation for about 15 keV while for practical microscopy 10 keV of primary energy is most suitable. In this case the overall working distance should be not less than 8 mm from which 5 mm is left for the CL field. In SEM instruments without specimen loading via an air-lock, it is usually easy to design an insulating insert cup into the standard specimen cartridge so that the specimen holder connects to a high-voltage contact via a pin passing along the stage axis. This design leaves intact all specimen movements including rotation. In air-locks the specimen cartridge is usually side inserted so that some additional mechanism is needed for contacting from the lower side of the specimen already loaded. Alternatively, the contact can be connected in the direction of the specimen loading and a flexible cable used between the specimen stage and feedthrough. These designs have to be tailored to a particular instrument and to its full setup with all options and attachments. The specimen biasing itself needs a negative supply with a ripple not exceeding 10-5 of the output voltage, finely adjustable in steps of 1 eV or smaller. Because the supply is usually operated near its maximum output voltage, the parameters should be assessed for the full scale. Generating the low landing energy of electrons via the difference between two high voltages is obviously not an optimum solution not only because of the addition of instabilities of the two supplies; it would be more advantageous to apply a voltage directly between the gun cathode and specimen. However, for CL applications this supply would have to be designed as passing smoothly through the zero voltage to the opposite polarity, e.g., during alignment, which is a feature not available with commercial laboratory supplies. The alternative and better solution consisting in using the beam booster (an insulated and positively biased tube around the optical axis between the
SCANNING LEEM
"booster". , insulator ~ magnetic ~ . ") objective ~I lens
401
,,o+ U
"I > >
\xi
-\
\
\
\
specimen
\
\
N
,
I
I/'/
~
I
/
/
/
/
/
/
/
I
,/
/
9
/
/
FIGURE 45. Possible design of a booster inserted into a magnetic pinhole lens. (Adapted with permission from Beck et al., 1995.)
gun anode and bottom of OL, see Figure 45) is mostly reserved for dedicated instruments but adaptation of this type to a conventional SEM was also reported (Plies et al., 1998). Let us explicitly state an obvious fact that with a commercial SEM containing the booster, the adaptation to the CL mode might be restricted to mere removal of the final electrode of the IOL or to its connection to the upper electrode; in this way the retarding field is shifted to between the end of the booster and specimen.
B. Dedicated Equipment
To the authors' knowledge, among general purpose SEM instruments marketed at present no IOL-containing dedicated device exists except the 1500 Series SEM of LEO Electron Microscopy with the Gemini lens shown in Figure 22 (see http://www.leo-usa.com). The new type of JSM-7400F of JEOL already incorporates specimen biasing but only to 1 to 2 kV and the purpose is declared to consist solely in acceleration of SE toward an electron converter where they are transformed to tertiary electrons detected by the upper detector (Kazumori, 2002). Probably all recent IC testers, i.e., specialized SEMs with very high beam current and a scope of operation modes tailored to inspection of semiconductor structures, including measurement of critical dimensions and local voltages, generation and sensing the electron-beam-induced currents, and operation with surface charges compensated by controlled
402
MOLLEROVA AND FRANK
Schottky cathode i
anode
i
SPCL
diaphragm
0=41=0
VVien filter 1
-
"~j
I
upper S E detector
I SPIOL
W i e n filter 2
scanning coils "''""
j lower SE detector
FIGURE 46. High-probe-current, low-energy SEM column equipped with a single-pole condenser lens (SPCL) and a single-pole objective lens (SPIOL) (see text for details). (Reprinted with permission from Beck et al., 1995.)
back-streaming of SE, are solved with immersion objective lenses (see, e.g., Meisburger et al., 1992; Miyoshi et al., 1999). Let us describe two of these solutions in more details. Beck et al. (1995) summarized problems connected with the formation of high-current low-energy probes and designed the dedicated column shown in Figure 46. It incorporates the central booster at + 9 kV (consisting of the gun anode and electrodes 1 to 4) so that with the Schottky cathode at - 1 kV and specimen at ground, the primary beam is held at 10 keV throughout the column but within the CL is retarded to the final 1 keV. Using singlepolepiece configurations both as the condenser lens (Cs= 13.2 mm, C c = 11.5 mm) and objective lens ( C s = 1.05 mm and Cc=0.83 eV at a
SCANNING LEEM
403
working distance of 8 mm and focal length 5 mm, when the retarding field is taken into account), they reached the calculated spotsize of 46 nm and the measured resolution of 50 nm. The beam current was calculated to reach 150 nA but measured only 20 nA, which was ascribed to insufficient vacuum conditions in the gun chamber. The lower SE detector was used only with an unbiased booster while in the low-energy mode the accelerated SE are deflected in the lower Wien filter to outside electrode 2 so that they can impinge on the upper SE detector. Although the Wien filter did not deflect the primary beam, it caused dispersion, astigmatism, and some higher-order aberrations that required pre-compensation by the upper Wien filter with opposite orientation. Meisburger et al. (1992) used the primary beam at 20 keV in the column and decelerated it in front of the specimen held at -19.2 kV together with the nearest electrode of the immersion objective lens that was combined with a magnetic single-polepiece lens below the specimen. Again a resolution of 50 nm was achieved at the landing energy of 800 eV with 50 nA in the probe. As above, two Wien filters were incorporated of which the lower one deflected signal electrons to a semiconductor detector with a fiber-optic light guide while the upper Wien filter incorporated in its electrostatic octupole the blanking unit, stigmator, and centering system. More instruments of the type described above can be found at major producers of SEM technology and also a specialized instrument industry for this application exists. Nevertheless, critical details about equipment developed outside the academic community are very often confidential. Another family of dedicated instruments consists of laboratory equipment composed for basic research tasks and although their development often began with a commercial microscope, the volume of modifications was much larger than that described in the previous section. One example is the UHV SEM working within the range 100 eV to 3 keV with resolution of 60 nm at 250 eV and equipped with a LEED pattern detector consisting of two concentric hemispherical grids, two microchannel plates, and a two-dimensional detector. The specimen was typically inclined 45 ~ toward the detector that was, moreover, rotatable around the sample. Signal processing functions included selection of a diffraction spot for the brightfield imaging and for various dark-field images. This device, based on a Hitachi S-800 but completed by equipment typical for surface analysis devices including the magnetically driven transfer from the air-lock, provided many interesting observations, e.g., of grains on polycrystalline Si, the step structure on a Si (111) surface, domain structure on the reconstructed Si (110) 16 x 2 surface (Ichinokawa et al., 1987), and also of superstructures and of movement of islands on an Au-evaporated Si (111) surface (Ichinokawa et al., 1986). In order to collect and process the image
404
MOLLEROVA AND FRANK
FIGURE47. UHV SLEEM for examination of clean and defined surfaces (the magnetically driven specimen transport is not attached to the air-lock on the far right-hand end). data, the authors of these studies made enormous effort with their electronic equipment, the quality of which was far below that of the present. In the authors' laboratory an UHV SLEEM instrument has been developed, the design representing a combination of the "adapted SEM" outlined above (i.e., biased specimen and detector according to Figure 37) and facilities usual in surface analysis equipment for examination of clean and defined surfaces (clean UHV conditions of the order of 10 -8 Pa, separate preparation chamber with the ion gun for cleaning and sputtering the surface, and with an attachment for evaporation of m e t a l s ) see Figure 47. The basic illumination system is the commercial electrostatic two-lens column with a Schottky cathode (2LE Column, FEI Company; see http://www.feibeamtech.com/pages/electron.html). The apparatus is intended to employ diffraction, interference, and energy-band contrasts and will be equipped with a two-dimensional LEED pattern detector the design of which has not been finished yet and with a parallel operating electron
SCANNING LEEM
405
FIGURE 48. Double-tilt specimen stage for the device in Figure 47, permitting insertion of a specimen cartridge via the air-lock with five high-voltage connections to outside of the vacuum chamber.
energy analyzer of the hyperbolic type (Jacka et al., 1999) that is under preparation. As we saw in Section VI.E, even a tiny specimen tilt manifests itself with large beam impact angles at the lowest energies. In order to acquire full control over the impact direction, a double-tilt specimen stage is necessary as shown in Figure 48. It features the x and y movements of + 5 mm, z-axis movement of 4- 10.5 mm, rotation of -t-8 ~ and two mutually perpendicular tilts of up to + 5~ One prospective task is to solve a combination of the SLEEM method with surface microanalysis like Auger spectromicroscopy. For this purpose a miniature all-electrostatic SLEEM column has been developed with the built-in detection part shown in Figure 34(b) (see Frank et al., 2000a). The whole device (see Figure 49) is of length 90 mm and diameter 45 mm, and at 5 keV primary energy, probe current of a few nA, and working distance 5 mm, it provides a resolution of 30 nm (E1-Gomati et al., 2002) that predicts a value around 100 nm at 10 eV. The column fits inside a cylindrical mirror analyzer for Auger electron spectroscopy but in a separate installation it can be completely biased to a high positive potential providing for the CL configuration with earthed specimen. Bearing all the previous considerations in mind, we can now outline a design for the ideal dedicated SLEEM instrument for general
406
MULLEROVA AND FRANK
FIGURE 49. Electrostatic three-lens mini-column, equipped with Schottky cathode, two-stage quadrupole centering system, octupole stigmator/centering and built-in detector (see Figure 34(b)) with a six-segment collector. (Reprinted with permission from Frank et al., 2000a.)
very-low-energy SEM applications. Such a device would be similar to the setup shown in Figure 46, i.e., equipped with the positively biased booster and the CL with the specimen at ground potential. For acquisition of diffraction and energy-band contrasts, a two-dimensional multichannel detector is desirable onto which the full LEED pattern would be projected. In order to focus the diffraction pattern, we have to let the signal beam pass through some lens. This can be an IOL and then deflection toward some kind of upper detector is necessary but here the deflection assembly has to image its input plane onto the detector plane, so that behind a weak Wien filter the simple extraction field has to be replaced by regular large-angle deflection unit. Altogether the device becomes relatively complicated so that
S C A N N I N G LEEM
407
a configuration with the single-polepiece lens inserted below the specimen (e.g., a miniature one with permanent magnets) seems to be more promising. Then, the LEED pattern will be formed in the space between the specimen and the SEM column (Mfillerovfi and Lenc, 1992b). Having ample free space available (see Figure 36), we can design the two-dimensional detector on various principles. Of course, the specular beam would still escape detection, but this could be avoided by allowing for a small specimen tilt. Naturally, a field-emission gun of a high brightness is desirable and when designing the specimen chamber as a UHV one, we extend significantly the scope of possible applications.
C. Alignment and Operation If a conventional SEM is adapted via insertion of the CL, the routine procedures for alignment and operation become modified. Let us now make a few remarks on this topic. A key issue is the strong electric field in the specimen chamber. The maximum applicable strength of the field between the specimen and anode within the CL naturally depends on the quality of both surfaces. It is generally recommended to arrange the specimen holder or cartridge so that no sharp edges or protrusions appear on the side facing the anode and to cover the specimen with a large flat cap made of a smooth foil, leaving the desired part of the specimen exposed for observation. It is good practice to start the experiments with every new specimen by "training" the specimen biasing by slow stepwise increase of the voltage with the rest of the microscope switched off. Good optical properties are obtained for sufficiently high values of the immersion ratio k so that the primary energy should not be chosen below 5 keV while 10 keV seems to be an optimum value. Thus, the field strength is mainly controlled via the working distance and according to experience the range between 1 and 2.5 kV mm -1 (i.e., l between 4 and 10 mm) usually suits the purpose. Naturally, when predicting the imaging parameters dependent on the working distance, we have to take into account the necessary underfocusing of the SEM column, connected with the CL optical power (see the next section). We now restrict ourselves to the configuration shown in Figure 37 that has proved to be optimum for adaptation of general purpose SEMs. Two points are important here, namely aligning the detector onto the optical axis and tuning the homogeneity of the CL retarding field. The detector alignment is a standard initial routine used not only when the detector is designed to be retractable as was recommended above but always before entering the SLEEM mode. This routine should be performed
408
MULLEROV,~ AND FRANK
FIGURE 50. An example of the appearance of the microscope screen when the detector/ anode assembly shown in Figure 37 is being adjusted onto the optic axis: (a) the upper surface of the YAG crystal with no specimen bias and only low BSE signal from a specimen composed of light elements; (b) the YAG surface combined with the specimen image in the bore, both images being defocused with the sharp image plane situated between them (specimen biased for an impact energy of 1 keV so that the SE signal dominates).
with a perfectly aligned column, particularly as regards the beam centering. The upper surface of the YAG crystal is treated in the same way as the lower detecting surface so that at low magnifications the scintillator material around the central bore is struck by primary electrons from above and the YAG surface is visible on the microscope screen as a bright area with black circular feature, which can then be easily mechanically adjusted to the screen center (see Figure 50). When afterwards increasing the magnification, we restrict the scanning range to within the detector bore and only the lower YAG surface remains active for electrons emitted from the specimen. This low limit of magnification is usually between 250 and 500, which is one of the drawbacks of this detector type. Nevertheless, modern computercontrolled microscopes enable one to control every active element within the column easily so if a larger field of view is needed, the pivot point of the deflection system can be shifted nearer to the scintillator. This change increases the OL aberrations because of an out-of-axis passage of the beam but the corresponding drop in resolution should not be perceptible owing to the enlarged pixel size. A further step in the recommended procedure is to check whether the position of the detector bore does not move on the screen when refocusing from the detector plane to the specimen plane visible inside the bore; otherwise the OL centering has to be improved. Next the specimen bias is increased in steps and image astigmatism is corrected together with the shift
SCANNING LEEM
409
FIOURE 51. An example of the very-low-energy image in the center of the field of view with the rim of the mirror image connected with glancing electron impact and with their reflection in front of the surface; electron energies from the left: 2.5, 1, 0, and -2.5 eV.
of field of view, which is eliminated via slight specimen tilt. When continuing this until the specimen bias is equal to the gun voltage, we approach the zero energy of electron impact so that from the margin of the field of view the surface image starts to convert to the mirror image of an above-specimen equipotential surface. Now the most sensitive alignment of the CL field can be made by shifting the residual central area of the very-low-energy image into the screen center by using small specimen tilts. If the double-tilt facility is not available, the single tilt can be combined with the specimen rotation. Sometimes small corrections of the OL centering are made but this is a pragmatic step not belonging to the consistent alignment procedure. This step of the alignment procedure is illustrated in Figure 51. Roughly below 5 eV some signal decrease in the center of the field of view starts to appear owing to loss in signal escaping through the detector bore, as follows from Figure 38. At low magnification, the margin of the field of view appears (see the next section, Equation (60)) and shrinks with further reduction of the energy. Around the field of view, a rim of mirror image is seen where electrons reflect on above-surface equipotentials. When the zero energy is reached, the specimen surface acts as a planar mirror reflecting the lower scintillator surface with the central sink and bore and this image can be focused. The signal deficit in the center of the field of view, analogous to the escape of the (00) diffracted beam, is inherent in coaxial detectors in general. In practice this is avoided by a slight specimen tilt causing only a small loss in resolution. Systematic solution requires using a deflection unit and sidepositioned detector. In a well-aligned device, the very-low-energy image centered according to Figure 51 is seen and the field of view does not move when decreasing the specimen bias throughout its full range. In Figure 51, some residual ellipticity of the central spot is still visible, which indicates that the configuration is not perfectly axially symmetric.
410
MULLEROVA AND FRANK
In the course of the SLEEM mode operation it is always wise not to increase the specimen bias too fast and to use specimen movements, z-shift, tilt, and rotation in particular, very carefully with larger changes better made at a low bias. Interpretation of contrast observed below a few hundreds of eV is often not straightforward and is significantly facilitated when a series of micrographs of the field of view is available within the full energy scale. D. Practical Issues
The optical power of the cathode lens influences the beam impact on the specimen and modifies characteristics like the image magnification, the working distance (when assessed according to excitation of the magnetic focusing lens), and the impact angle connected with beam rocking around the pivot point of the scanning system. Also an additional condition restricting the field of view appears, namely that connected with the increase of the impact angle to rt/2 as is shown in Figure 51. While the restriction to the field of view and increase in the impact angle can be only recognized and considered when interpreting the image, corrections for focus and magnification should be incorporated into the microscope control software. This section aims at preparing algorithms for these corrections (see Zoba6ov~t et al., 2003). The basic equations were given by Mfillerov~ and Frank (1993) while Huta~ et al. (2000) solved the correction of magnification. Let the primary beam trajectory (see Figure 52) be initially directed into a point with radial coordinate r0 that in paraxial approximation is given as r o - ( w s + l ) f l , where Ws is the axial coordinate of the virtual vertex of the scanning system. The field in the anode bore acts as a diverging lens of a focal length fA that moves the virtual vertex to Z----Wst=fAWs(WS--fA)-1. The lens also enlarges f l ~ f l ' and in the paraxial approximation (i.e., when we can put tan fl = sin/3 ~ fl), we get
~ ' - ~ Ws/W~. The homogeneous retarding field further deflects the oblique impacting ray along a parabolic trajectory so that it is easy to trace its radial coordinate and velocity; an interesting point is where the axial velocity falls to zero. This takes place on a fictitious "reflection surface" that intersects the specimen surface at a radial coordinate rmax defining the maximum size of the field of view to Vmax - 2rmax ~
4l 4l + 3ws ~ . 4l + WS
(60)
SCANNING LEEM
411
FIGURE52. The primary beam trajectory inside the objective and cathode lenses. In order to derive Equation (60), the focal length of the aperture lens (Lenc and MiJllerovfi, 1992a) k f A -- --41 k---f-~
(61)
was, for near-zero landing energies, i.e., k > 104, approximated by -41. Assuming W s = 25 mm (see below), l = 5 mm, and E e = 10 keV, we get Vmax = 0.42 mm at the landing energy of 1 eV and 130 gm at a mere 0.1 eV, i.e., quite acceptable figures. It is obvious from Figure 52 that the beam impact angle, which is initially equal to/3 and, owing to the aperture lens action, enlarges to/3', increases further within the retarding field. Solving again the parabolic motion up to the specimen surface, we get for the final impact angle, [3cL, the relation tan/3cL =
sin/3' v/ 1 - k sin 2fl'
,
(62)
412
M(JLLEROV,h. AND FRANK
i.e., this enlargement is roughly k ~/2 times. When substituting for/3' and then from Equation (61), we find near the optic axis
~ CL -
r ~~/--~ WS + I
1 -}
~
W S
k
-~. .
(63)
For a tilted specimen, this impact angle, increasing linearly with the off-axis distance, combines with the uniform impact inclination shown in Figure 44. The above-described changes in the parameters of the field of view are inherent in the configuration and although we can modify them to some extent by controlling the vertex position ws, actual correction for them is neither possible nor desired. On the contrary, changes in magnification and in the efficient working distance should be automatically corrected in the control software. In the paraxial approximation the coordinate rc of the impact point (see Figure 52) amounts to r c = ( 2 1 e + Ws')fl' with e = k l / 2 / ( 1 + kl/2). Let us define the magnification correction factor A M = ro/rc < 1, which can be used for updating the size of micron marks or the numerical magnification values. From previous relations we can write this as AM =
fA(Ws + l)(~/-k + 1) . fA WS(~/-~ + 1) + 2lVCk(fA - ws)
(64)
It should be noted that A M does not represent the CL magnification, which is, of course, not Ws dependent. When substituting forfA from Equation (61), we get at k >> 1 the factor A M e (1/2, 2/3) within full range of ws/l; the most often met value is A M ~ 0 . 6 . Careful measurement of A M showed that the approximation (61), derived while considering an abrupt change of the CL field in the anode plane, does not provide values o f fA fitting the measured data with accuracy sufficient for the purposes of critical dimension measurement for example. Hence a more exact relation was derived, based upon modeling the anode field of a finite thickness t within which both the axial potential and the electron trajectory follow parabolic curves. Lenc and Mtillerov~i (1992b) used this approach when deriving relations (42) and (43) for the CL aberrations. The result was k X 4 - ln(1 - X2) - 1 , )CA---41 k- 1 2 Arth X
E
I
X --
k
It 1"
(65)
SCANNING LEEM
413
Finally we will look at the magnitude of underfocusing Af that has to be made with the magnetic OL when the cathode lens is excited. In a similar way as above, we find in the paraxial approximation that the surface point is imaged by the retarding field at a distance 21e below the anode. The aperture lens in the anode plane further images this virtual crossover so that it appears near a point lying at a distance of 1/3 below the specimen; more accurately, the axial shift of the focused probe is given by
A f -- --l 21x/k + fA ( ~ -- 1) > 0. 21x/-k -- f A (~/-k + 1)
(66)
In order to obtain a rough quantitative estimation, we use fA from Equation (61) and k >> 1 and get A f ~ ( l / 3 ) [ 1 - ( 8 / 3 ~ ) ] . This leads to a slope of the refocusing, necessary when the energy varies, expressed as 3(Af) ~ -
OE
-
41 9~/EpE
o
(67)
For example, with l = 5 mm and E p = 10 keV we get 7 gm eV -1 at 10 eV. Equations (64) and (66), each in combination with Equation (65), represent the desired algorithms for the on-line correction of magnification and for the refocusing. Both algorithms contain three parameters, Ep, l, and t, while A M depends also on the vertex position Ws. Values of t and Ws cannot be directly measured and in fact they represent some effective dimensions obtainable only by fitting experimental data to the model. This was made in one particular SLEEM arrangement and the result was Ws= 25.62 mm (with the OL aperture situated at 27 mm above the anode) and t-- 5.79 mm for an anode bore of D = 3.5 mm. The ratio t/D = 1.65 for an anode thickness of 2 mm corresponds accordingly to a ratio of 1.25 for a thin anode (Lenc and Mfillerovfi, 1992b). Furthermore, for a broad range of variables the measured magnification factors AM(l, E) fitted the above model with deviations below 1.9% including the measurement errors (Huta[ et al., 2000).
VIII. SELECTED APPLICATIONS
This section summarizes the results of some demonstration experiments in which the aim was to map the main features of SLEEM micrographs at low and very low energies for a particular family of specimen types and
414
MOLLEROVAAND FRANK
to verify the feasibility of obtaining the types of contrast inherent in slow electrons. Only in Sections VIII.D and VIII.I do we quote results of more systematic studies.
A. Prospective Application Areas First of all let us briefly characterize the application areas in which the use of the SLEEM mode can contribute to progress in the solution of research tasks. It is well established that examination of semiconductor structures, both as regards their geometry and critical dimensions and the local voltages and currents, either initiated by powering the structure or induced by the electron beam, is best performed at beam energies around 1 keV. Dedicated IC testers use this energy and many of them are equipped with some retarding field element. The doping contrast is highest around 1 keV, too, and a further possibility is to use the elastically backscattered electrons at a tailored very-low-energy causing no damage. Nonconductors were for a long time observed below their critical energy where only a moderate charging takes place. This mode was, of course, surpassed by observation just at the critical energy, as described in Section VIII.D. However, a new approach has arisen consisting in controlled return of the fraction of SE needed to balance the charge so that the noncharging situation can be secured at any energy but still only below Ec2. Detailed examination of surface topography is best made at an electron energy for which the interaction volume inside the specimen fits in size the relief protrusions. To a certain extent this remains valid even at energies for which the primary electrons do not penetrate to below the escape depth of SEmif a raised feature is just filled with the interaction volume, even SE directed quite far from the surface normal might be emitted. For details smaller than 100 nm this means that the low-energy range must be used. These small features replace the topographical contrast of inclined facets and surface steps, dominating at high energies. Variations in the electron yield with crystal orientation culminate at a few hundreds of eV, which energy range is then optimum for observing grains in polycrystals, crystallinic precipitates, and amorphized areas in crystals. The diffraction and interference contrast below, say, 20 or 30 eV reveals phenomena connected with surface crystallinity and its changes owing to surface reconstructions, adsorption, desorption, growth of layers, sublimation, diffusion, segregation, etc.
SCANNING LEEM
415
This list obviously covers selected but very numerous tasks from virtually any of the application fields of microstructure examination, both in materials science and the life sciences.
B. General Characteristics of Micrograph Series Because of the lack of experience with contrast appearing in micrographs below, say, 500 eV, it is good practice to acquire always (or at least with a new type of specimen) a series of micrographs beginning with the primary beam energy used and continuing by increased specimen bias, possibly up to near the zero energy. When doing this, attention should be paid to preserving the identical field of view and to correcting for the magnification changes wherever this is not performed automatically. This micrograph series will show some characteristic features that include disappearance of the edge effect, transformations in the material contrast, and enhancement of the relief contrast. Further image changes with decreasing electron energy are then inherent to individual structure types. One example is seen in Figure 53, which shows the surface of a Cu polycrystal with the surface oxides and contaminants removed by chemical etching. While at 5 keV the image is strongly dominated by the edge effect appearing on steps made by etching along grain boundaries and also on other etch pits, at 200 eV these over-brightened features are not visible. Instead, the fine surface relief combined with the grain contrast appears as most pronounced. At 10 eV the contrast of residual islands of
FIGURE53. Surface of a polycrystalline Cu sheet etched in nitric acid, Tesla BS 340 SEM adapted for the SLEEM method, energies from the left 5 keV, 200 eV, and l0 eV, the width of the field of view is 70 gm. (Reprinted with permission from Miillerovfi and Frank, 1994).
416
MOLLEROVA AND FRANK
FIGURE 54. GaAs-based integrated circuit, JEOL JSM T220A SEM adapted for the SLEEM method, electron energies (a) 9800 eV, (b) 4300 eV, (c) 1400eV, (d) 20 eV; the width of the field of view is 400 gm. contamination is strongest; the mechanism would require further examination in order to be explained, a surface microanalysis in particular. Another typical example, shown in Figure 54, represents the semiconductor structures. Here one can notice primarily the contrast changes caused by decreasing penetration depth as interfaces between technological layers are crossed, which projects itself into variations in the BSE and SE2 yields. Possible dynamic effects, connected with injection of electrons into interface states and creation of space charges within the information depth, would also need further examination. At 20 eV the local charging and surface details and defects are most obvious. This micrograph series also illustrates the noncorrected changes in the image magnification with decreasing electron energy. The third example in Figure 55 consists of only a single micrograph representing a typical example of an unexpected contrast that appeared at low energies without being apparent at all at 10 keV. The dots arranged in rows on a cleaved GaAs crystal surface might represent islands of oxide layer preferentially grown on crystal defects or on edges of surface steps made when cleaving but no reliable explanation is at hand. Again, surface microanalysis would greatly facilitate the interpretation.
SCANNING LEEM
417
FIGURE 55. "Decoration dots" on the fracture surface of a low-quality GaAs crystal, Tesla BS 343 SEM adapted for the SLEEM method, electron energy 250 eV, the width of the field of view is 20 gm.
C. Surface Relief In all the series of micrographs in this section, strong enhancement of the relief contrast is apparent when they are made within a broader energy range. At flat metal surfaces without any artificial structure, small relief details are best visible around 50 eV where the penetration depth is shortest. In Figure 56 two frames from the first published series of micrographs, taken throughout the full energy scale, demonstrate this trend. We notice here that although the detector system shown in Figure 37 that was used to acquire the majority of the micrographs is of the overhead type and should not produce any shadowing effects, in practice this is not entirely true. The scintillator is placed in an axially symmetrical position but the side-attached light guide breaks the symmetry and the efficiency of light transport is not identical all over the scintillator crystal even if the optical contact is made properly. Owing to the strong acceleration within the CL field, the emitted electrons more or less preserve their off-axis coordinates and species emitted from any one pixel impact the detector locally. Consequently, the image side situated below the light guide is the brightest (see Figures 50 and 51) and sometimes some off-line corrections are needed at very low energies. In connection with this, larger surface facets inclined toward the light-guide direction might also exhibit a higher signal and hence some kind of moderate shadowing is observed.
418
MOLLEROV~i.AND FRANK
FIGURE56. Chemicallyetched polycrystallineTi sheet, Tesla BS 350 UHV SEM adapted for the SLEEM method, electron energies 15 keV (left) and 50 eV (right), the width of the field of view is 50 ~tm.(Reprinted with permission from Mfillerovfiand Frank, 1993).
D. Critical Energy Mode In Section III.E, we discussed phenomena connected with charge accumulation in nonconductive specimens and saw that if the total electron yield curve cr(E) is taken as the process diagram, then spontaneous movement of the working point toward the critical energy Ec2 does qualitatively explain the observed effects. In addition, it was argued that when the electron energy is below Ec2 , the ultimate (positive) surface potential is reduced because of recapture of the slower part of the SE. It is important to recall that, irrespective of the initial energy of impact, the charging process causes shifts of the impact energy, influenced by fields of persisting charges, directed always toward Ec2. This is, of course, connected with corresponding changes in the image signal; Figure 57 illustrates this for the alternative of a positive charging up. This is a well known effect encountered in the observation of nonconductors and can be utilized via a practical procedure consisting of a temporary increase of the image magnification and subsequent relative assessment of the signal level from the smaller field of view with respect to its surrounding, which reveals in what direction the charging has changed the average emission (see Joy and Joy, 1996). The same approach forms the basis for an automatic method of determination of Ec2 (or, more exactly, of the energy causing minimum damage of the image owing to charging), which is also outlined in Figure 57. The method (see Frank et al., 2001) consists in acquisition of a temporal sequence of image signals from individual pixels since their first illumination, and in off-line determination of the integral under the S(t) curve, which can be taken as a measure of the total signal change caused by the charge accumulation. By plotting this quantity versus the initial impact
SCANNING LEEM
.
.
.
.
,
.
419
.
I IMPACT m I ENERGY ! !
Ec,
E8
Ec~
E
t2 S
Q
,%o t
Ec~
E8
FIGURE 57. Scheme of the spontaneous time development of the image signal in the course of positive charging up: movement of the "working point" from initial (Es) to final (EF) impact energy (top), signal vs. time plot (bottom left), and the area below the S(t) curve (the charging rate) as a function of the initial impact energy (bottom right). (Reprinted with permission from Zoba6ovfi and Frank, 2003.)
energy, we can find its optimum value where the curve crosses the zero level. The peculiar behavior of this curve below Ec2 was explained as a consequence of SE being "focused" into the detector bore by the radial field component above the charged field of view surrounded by the noncharged specimen (Zoba6ov~t and Frank, 2003). The results, demonstrated in Figure 58, are more reliable for flat specimens exhibiting only moderate heterogeneity in the conductivity and electron yields. The observation method described in this section requires modifications in the SEM control software that go beyond the scope of a simple adaptation made by the customer. It is mentioned here to demonstrate that, when working just at the critical energy, we can achieve much better results than at low energies in general. The same idea led to the above-described detection approach incorporating controlled return of a portion of the SE.
E. Diffraction Contrast In Section IV.B, we dealt with the electron backscattering from single crystals and hinted at the possibility of obtaining image contrast connected with locally varying fulfillment of the diffraction condition. This consists in getting a bright albeit defocused diffracted beam(s) incident on the detector, which is, for the detector types described here, achieved automatically except for the specular spot (00). Although at very low energies the reciprocal lattice is theoretically two-dimensional and bright spots are
420
MULLEROV,~i AND FRANK
FIGURE 58. Surface of writing paper, nonprocessed and uncoated, Tesla BS 343 SEM adapted for the SLEEM method, electron energies (a) 3650 eV, (b) 2650 eV (the critical energy Ec2), and (c) 1850 eV; the width of the field of view is 40 gm. (Unpublished micrographs courtesy of M. Zadra~il.)
received at any energy, in fact significant variations in the spot brightness with electron energy are always observed. Consequently, the eBSE signal from crystals is modulated along the energy scale according to the crystal orientation and the distance from the Ewald sphere of a nearby reciprocal lattice point. Also, additional features can appear owing to effects going beyond the kinematical diffraction theory. The first test experiment was published and interpreted in detail by Frank et al. (1999). In Figure 59 we see micrographs taken at normal impact of the slow electron beam. One can compare the brightness of rectangular (with (100) orientation) and triangular (with (111) orientation) Pb crystals on Si and verify that it varies with energy in different ways in the two cases; this difference can be correlated with the diffraction condition for individual configurations. The interpretation of Figure 60 in which the micrographs are taken with the specimen tilted by a mere 1.3 ~ is much more sophisticated.
FIGURE 59. Flat Pb islands deposited in situ onto an Si (100) surface, JEOL JAMP 30 UHV SEM adapted for the SLEEM method, electron energies (a) 5, (b) 12.5, (c) 42.5, and (d) 378 eV, the width of the field of view is 60 gm. (Reprinted with permission from Frank et aL, 1999.)
SCANNING LEEM
421
FIGURE 60. The same specimen and microscope as in Figure 59, the specimen tilted to approximately 1.3~ in the direction inclined at 55~ with respect to the horizontal line, electron energies from the top left by rows: 6.5, 7.5, 10.5, 16, 18, 22, 29, and 34.5 eV; the width of the field of view is 50 gm. (Reprinted with permission from Frank et al., 1999.)
Now, not only the crystal orientation and energy but also the impact angles, both polar and azimuthal, play a role as they define the incident ray orientation with respect to the reciprocal lattice. Hence even crystals with an identical crystalline plane on the surface but mutually rotated exhibit some specific behavior of the eBSE signal with energy. In connection with this experiment, the degree of the illumination coherence was also assessed according to relations given in Section IV.C. The size Dc of the coherently illuminated area was determined according to Equations (29), (31), and (32) and also the condition (30) for the source size was verified. The experimental data were taken as A E = 0 . 5 eV, E p = 10 keV, a c = l mrad, E = 1 0 eV, and dhk=3 nm. Considering the OL demagnification to be 10 times, we have or0 = 0.1 mrad for the diaphragm illumination angle in Figure 15, and finally we get ot = 30 mrad for the aperture angle on the specimen. Then the factors limiting Dc result as IAsl = 15.5 nm, we = 12 nm, and wo= 6.4 nm for 0=re/2 with increase to 9.1 nm at 45 ~ The real spotsize was not measured but could be estimated to be between 10 and 20 nm. Obviously, the constructive interference took place at least for a major part of the primary spot, which means that at
422
MOLLEROV,~i AND FRANK
favorable conditions the image signal was increased by a factor approaching the number of unit cells within the coherence area or within the crystal domain, whichever is smaller. It is obvious that observations like these can be made solely on very clean surfaces and under true UHV conditions. However, it should be underlined once more that these demands do not arise from the observation method employing very slow electrons but they condition the phenomena that can be observed. Prospective applications of the diffraction and interference contrast mechanisms can be estimated according to the huge variety of experimental results collected by means of the LEEM apparatus (see, e.g., Telieps and Bauer, 1985; Telieps, 1987; Bauer and Telieps, 1988; Tromp and Reuter, 1993; Tromp et al., 1993; Bauer, 1994; Tromp, 2000). A survey of references in this area can be found at http://www.leem-user.com.
F. Contrast of Crystal Orientation In the previous section the examples showing a crystallinic structure in verylow-energy micrographs concerned the coherent backscattering when the detected yield is increased by amplitude instead of intensity addition of scattered waves. However, in Sections IV.B and IV.D we also mentioned the dependences of both BSE and SE yields on the crystal orientation and argued that these should become more pronounced at low energies. In fact, experiments showed that for metal polycrystals the grain contrast in SLEEM images is highest between 50 and 150 eV (see Figures 53 and 56). Another application of the same effect arises when amorphous and crystalline areas are to be distinguished. The example in Figure 61 presents a lattice of spots amorphized by laser beam exposure of a crystalline layer. Owing to this amorphization, a decrease in both SE and BSE signal can be generally expected so that brighter centers of dots, caused by increased laser beam power, need to be examined in more detail. Figure 61 illustrates the enhanced sensitivity of slow electrons to spurious a.c. electromagnetic fields. The vertical stripes are caused by an excessively high amplitude of the 50 Hz interference from the SEM electronic console.
G. Layered Structures One trivial consequence of lowering the impact energy is that thin surface layers that were transparent at high energies become opaque and their structure can be observed. The example in Figure 62 shows a trilayer structure prepared for exploration of the backscattering factor in Auger
SCANNING LEEM
423
FIGURE 61. Structure created by laser beam exposure of microdots (with various beam intensities and exposure times) in a Pt3Si layer made on a glass substrate, dot pitch 2.9 ~tm; Tesla BS 343 SEM adapted for the SLEEM method, electron energy 200 eV. (Specimen provided by Dr. H. Birecki, HP Labs; reprinted with permission from Mtillerovfi, 1996.)
FIGURE 62. A patterned multilayer structure consisting of islands of a 500 nm thick Au layer (right) on a Si substrate, partially covered with a 200 nm thick layer of GeSi (top left), JEOL JSM T220A SEM adapted for the SLEEM method, electron energies 9800 eV (left) and 850 eV (right), the width of the field of view is 300 gm. (Specimen provided by Professor M.M. E1-Gomati, University of York, UK.) s p e c t r o m i c r o s c o p y ( E 1 - G o m a t i et al., 1992) w i t h a n o b v i o u s d e m o n s t r a t i o n o f this effect. S p e c i m e n s o f s e m i c o n d u c t o r devices in a p l a n view, like t h a t in F i g u r e 54, e x h i b i t t h e s a m e f e a t u r e s b u t c o m b i n e d w i t h o t h e r effects a n d h e n c e are n o t so striking.
424
MfOLLEROVA AND FRANK
FIGURE 63. A beveled cross-section cratered by oblique impact of a low-energy ion beam across a multilayer structure consisting of 12 pairs of 100 nm GaAs/63 nm AlAs layers; Tesla BS 343 SEM adapted for the SLEEM method, electron energies from the top left by rows: 20, 30, 40, 130, 430, and 2430 eV; the width of the field of view is 600 gm. (Specimen provided by Dr. J. Kovfi6, TU Bratislava, Slovakia, preparation by Dr. A. Barna, KFKI Budapest.)
Unlike the previous example, the structure in Figure 63 produces contrasts that are not so easy to understand. The beveled section of a multilayer, composed of two alternating different semiconductors, shows outcrops of layers of one material (GaAs instead of AlAs) at a strongly elevated contrast within a certain energy interval, and in addition three stripes of different intensity instead of two can be distinguished periodically repeating across the structure. One boundary of the "extra" bright strip, namely that next to the dark part corresponding to the thicker wedge, is not sharp, which indicates that the contrast source might be buried. And in addition, the effect, i.e., both the contrast enhancement and formation of the third fuzzy strip, is clearly of a dynamical nature as can be seen from Figure 64 where none of the previous effects appears at the lowest electron dose while both features progressively emerge with increased current as well as with prolonged frame time. Similar effects were observed with Mo/Si multilayers (Mfillerovfi et al., 1997) but they were absent at metallic multilayers such as Ni/Cr. The phenomenon will be further studied because the provisional interpretation, relying upon the influence of charges trapped in the interface states and forming a buried space charge layer, needs to be
SCANNING LEEM
425
FIGURE 64. The same specimen and microscope as in Figure 63; electron energy 450 eV, the width of the field of view is 600 gm, primary beam current 0.2 nA (upper row) and 80 pA (lower row), frame times from the left 3, 11, 30, and 83 s. (Reprinted with permission from Mfillerovfi et al., 1997.)
supported by more experimental data; furthermore a complete model of the contrast mechanism, even qualitative, is not available yet.
H. Material Contrast
The absence of the monotonic material contrast in the BSE emission, i.e., the direct proportionality 17 o( Z, available at conventional beam energies in SEM, is characteristic of the low-energy ranges. This fact is obvious from the t/(E) plots in Figure 13 for clean material surfaces. A comparison of clean and "real" surfaces in Figure 14 indicates that, under standard vacuum conditions and on specimens without any special treatment, some residual traces of this contrast can be observed down to about 1 keV. Below 1 keV any relations between BSE yields from different materials have to be specifically reconsidered. As Figure 29 shows, even the contrast between gold and carbon, otherwise representing the extreme in this respect, is inverted or at least disappears at 20 eV, where the eBSE emission already dominates. When following a particular combination of materials throughout the energy scale, even more than one inversion can be registered; Figure 65 shows two of them for the Cu/Si combination and both are met at energies for which the Cu layer is far from being penetrated so that no alternative explanation is possible.
426
MULLEROV,~ AND FRANK
FIGURE 65. Islands of a 300 nm thick Cu layer deposited through a mask, exposed by electron beam lithography, onto the Si substrate, period of squares is 10 ~tm; Tesla BS 340 SEM adapted for the SLEEM method, electron energies from the top left by rows: 5000, 500, 250, 100, 50, and 10 eV. (Specimen provided by Mgr. F. Mat~jka, ISI Brno, Czech Republic.)
On the other hand, for a particular couple of materials that at high energies exhibit a moderate contrast because of a small difference in atomic numbers only, in the low-energy range an energy value can be tuned for which much enhanced contrast is available (Mtillerovfi, 2001). Figure 65 also illustrates consequences of the bad practice consisting in performing the alignment, stigmation, and focusing inside the field of view selected for the final frame. Rectangles of the graphitic layer of contaminants, which are always formed on specimens but at high energies are usually transparent enough, heavily damage the images at low energies and particularly around 100 eV, albeit the sign of the material contrast remains preserved.
L Electronic Contrast in Semiconductors
Observation of doped areas with respect to the semiconductor substrate, both in plan view and on cleaved cross-sections, is one of the major tasks of microscopists, imposed by the semiconductor industry, which is faced with requests for continued diminution of the size of features and increase of the throughput. Several times we recalled the instrumentation branch of IC testers that are represented by low-energy SEMs with special sophisticated attachments. However, the basic question, how to get the best visualization
SCANNING LEEM
427
of the doped areas and what is the correct contrast interpretation, does not seem to have been definitively answered so far. It is obvious that no material contrast can reveal the dopant concentrations as low as 1016 to 1019 cm -3, when in a matrix of 5 x 1022 cm -3 of silicon atoms. Still, successful observations have been made since the mid-1990s and interpreted via the electronic contrast mechanism. Mtillerovfi et al. (2002) reviewed the previous studies and summarized the present situation in understanding the dopant contrast. The main points are that this contrast is observed in the SE emission, achieves up to 10% level when calculated from the equation
Cp/. -
S~
(68)
with Sp and Sn as the mean signal levels in p- and n-type areas, respectively, that p-type generally appears brighter than n-type, and that Cp/n grows toward low energies. In Figure 66 the main ideas are represented of the contrast model described by Sealy et al. (2000), which relies upon differences in the ionization energy; i.e., a distance between the valence band top and the vacuum energy. Because the tiny content of dopant cannot change this characteristic, the ionization energies Ep and E~ are considered identical but the local "vacuum" level varies in the model, being then balanced via abovesurface patch fields created by surface dipoles of nonconstant density. When the patch fields disappear at a distance comparable with the sizes of the doped areas, some average reference energy level is progressively reached sufficiently far from the specimen. A consequence is that electrons to be emitted from the n-type area have to surmount a barrier higher by some AE~. The flat band situation, shown in Figure 66, is modified when the presence of the surface states is taken into account, namely so that the band bending causes a drop in AE, and hence a contrast decrease. For the Fermi level pinned mid-gap at a high density of surface states, no contrast should be observed. The SLEEM observations were made on a boron-doped p-type patterned structure fabricated in an n-type Si substrate using two instruments with considerably different vacuum conditions (Mfillerovfi et al., 2002). The experiments (see Figure 67) confirmed the basic premises of the model, i.e., no BSE contrast and a moderate contrast in the SE emission. However, the most important finding was that significant increase in contrast was registered in the SLEEM mode. Careful contrast quantification verified the high contrast for the specimen inserted into the CL and revealed that even vacuum conditions play a very important role: at a standard vacuum of the
428
MULLEROVik AND FRANK
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Evac,p ESEM
Eil I .......
Evac,n
Ep
Ec,p En
Ec,n
X
EF
Ev, p Ev,n FIGURE 66. Combined band structures of p and n regions in the same specimen, with no influence of surface states assumed.
FIGURE 67. Boron-doped (1 x 1019 cm-3) p-type patterns on an n-type phosphor-doped (4 to 6 x 1014 cm -3) Si (111) substrate: (a) BSE image at 10 keV, (b) SE image at 10 keV, (c) SLEEM image at E~,= 10 keV, E = 1 keV; Tescan Vega 5130 SEM adapted for the SLEEM method, the width of the field of view is 350 gm for (a) and (b) and 500 gm for (c). (Specimen provided by Ing. B. Ne6asovfi, Tesla Sezam, Inc., Ro~nov p/R, Czech Republic.) o r d e r o f 10 -3 to 10 -4 Pa the c o n t r a s t clearly surpasses t h a t o b t a i n e d u n d e r clean U H V c o n d i t i o n s ( F i g u r e 68). T h e existence o f the e x t r e m e l y high c o n t r a s t for a specimen i m m e r s e d into a m o d e r a t e electric field n o t exceeding 2 V g m -1, i.e., w e a k e r t h a n fields n o r m a l l y applied to s e m i c o n d u c t o r structures u n d e r o p e r a t i o n , a n d the e n h a n c e m e n t u n d e r
S C A N N I N G LEEM
429
Cp/n [%] 20
10
102
103 E[eV] 104
FIGURE 68. The electron energy dependence of the SLEEM image contrast between p and n areas for the specimen shown in Figure 67; (A) dedicated UHV SLEEM microscope (see Section VII.B), (B) standard vacuum conditions, (C) SE signal from a standard ET detector. ((B) and (C) from Tescan Vega 5130 SEM adapted for the SLEEM method.) .
.
.
.
,
30
Cp/n [%] 20
iiii
10
ii
i
2
i
4
i
6
i
8
10
Ep [keY] FIGURE 69. The p/n contrast measured in the SLEEM mode for constant impact energy E = 1 keV but variable primary energy E/,.
routine vacuum conditions are facts very promising for application of the SLEEM method in semiconductor diagnostics and testing. The influence of the CL field is further illustrated by Figure 69 showing directly the contrast dependence on the field strength. The low-field limit obviously fits the contrast level achieved with the standard ET detector (see Figure 68). The crucial role of the vacuum conditions clearly indicates that the realization about the clean crystal surface as a base for the contrast interpretation is not correct. Further experiments showed that the contrast
430
MULLEROV~ i. AND FRANK
could be manipulated and even inverted by coating the structure with metals of various work functions. On this basis a new model was proposed (E1-Gomati et al., 2003) that considers the surface to be covered by a graphitic layer of contaminants with quasimetal properties and a metal-semiconductor junction to be formed beneath the surface. The subsurface fields, connected with the junction, explain successfully the observed phenomena even in cases when no patch field can be created, for example with the metalized surface that has to be taken as an equipotential one.
J. Energy-Band Contrast
In Section III.A.2, we described the reflection of very slow electrons on energy gaps, i.e., a contrast mechanism quite exotic from the point of view of SEM practice. In Figure 5 this was illustrated by measured energy dependences of the (00) spot intensity for two crystal orientations of tungsten. However, demonstration of this contrast in a SEM micrograph is difficult--any bicrystal and/or polycrystal specimens exhibit a combination of contrasts caused by phenomena anisotropic with respect to the crystal orientation so that reliably extracting this contribution is a problematic task. One exception is a semiconductor structure with patterned doping, observed in plan view. A clean semiconductor surface can be believed to possess identical properties on the doped pattern as well as on the substrate and the same holds for the crystal orientation in the sense that a small amount of dopant cannot change the electron yields. Nevertheless, additional impurity levels in the energy-band structure, namely those appearing in the energy gaps, can manifest themselves via this contrast mechanism. If such an energy level is hit, electrons penetrate into the doped pattern but not into the surrounding substrate so that the pattern appears dark. The first successful observation was announced by Mfillerovfi et al. (2001) and is shown in Figure 70. A signal decrease is apparent in micrographs taken at 3 and 1 eV and very pronouncedly in the 0.5 eV frame. This first experience has proved that this type of contrast is strongly dependent on even a tiny mechanical tilt of the specimen incorporated into the cathode lens. Figure 70 was taken with a provisional specimen stage with no tilt facility. Hence no true CL field alignment was possible and influences of inhomogeneity of the retarding field could be only compensated by suitable misalignment of the objective lens, which resulted in lowered resolution and enhanced axially nonsymmetric aberrations.
SCANNING LEEM
431
FIGURE 70. A p-type rectangle on the specimen shown in Figure 67, the SLEEM image at the electron energies from the top left by rows: 7, 4, 3, 2, 1, and 0.5 eV; dedicated UHV SLEEM microscope (see Section VII.B), the width of the field of view is 70 gm.
IX. CONCLUSIONS The element of instrumentation common to the history of work summarized in this text, the cathode lens, is in fact a very simple and very old assembly that can be easily incorporated into any electron optical device. In spite of this, it took more than 10 years before it started to appear frequently in the titles of papers in the journals devoted to scanning electron microscopy and its applications. The authors of this review feel a certain satisfaction about this development and about the forthcoming commercial devices containing this attachment, which may belong to the family of dedicated instruments for IC technologies or even to general purpose SEMs. Progress in this direction can break the "magic ring" and the increasing number of instruments will expand the community of users who quickly extend the application fields, etc. A U H V version of the instrument, equipped with devices for surface microanalysis methods, opens the way to examination of fascinating physical phenomena taking place on crystal surfaces that were revealed by the L E E M method. The scanning counterpart can take advantage
432
M(3LLEROVA AND FRANK
of multiple signal acquisition and simultaneous compilation of separate image slices for individual diffraction spots, possibly even completed by additional signals. More experienced users with some technical background can introduce the method into their commercial SEM instruments by an effort comparable with embarking on any other small nonstandard adaptation. For a boosterequipped SEM the adaptation might be quite trivial. In the near future, the first commercial SEM with the CL mode among the standard operation routines is expected. But, as for any other experimental method, the future progress of this method will also depend on its usefulness for a sufficiently broad community of users.
ACKNOWLEDGMENTS
This chapter reviews a major part of the work of the authors' team since the beginning of the 1990s. In the course of this time several particular projects have been brought to a successful conclusion under support of the Grant Agency of the Czech Republic and of the Grant Agency of the Academy of Sciences of the Czech Republic. The final period was supported by the GA ASCR grant no. A1065901. The results presented were naturally obtained in collaboration with other team members, both present and past, in particular Dr. Martin Zadra~il, Mr. Pavel Klein, and Mr. Mojmir Sirn~. The participation of other members of the Institute of Scientific Instruments of ASCR in Brno and the Institute's background in general were crucial for the whole long-term program. External cooperation was most intensive with Professor E. Bauer (TU Clausthal, Germany, and later the Arizona State University) and with Professor M.M. E1-Gomati (University of York, UK). The authors express their profound gratitude to all who helped them in their work. The final manuscript was compiled during a fruitful stay at the University of Toyama, Japan, for which sincere thanks are due to Professors S. Ikeno and M. Shiojiri and to Dr. K. Matsuda.
REFERENCES Autrata, R. (1989). Backscattered electron imaging using single crystal scintillator detectors. Scanning Microsc. 3, 739-763. Autrata, R., Hermann, R., and Mfiller, M. (1992). An efficient single crystal BSE detector in SEM. Scanning 14, 127-135.
SCANNING LEEM
433
Autrata, R., and Hejna, J. (1991). Detectors for low voltage scanning electron microscopy. Scanning 13, 275-287. Autrata, R., and Schauer, P. (1994). Behaviour of planar and annular YAG single crystal detectors for LVSEM operation, in Proceedings of the Thirteenth International Congress on Electron Microscopy, Vol. 1, edited by B. Jouffrey and C. Colliex. Les Ulis, France: Les 6ditions de Physique, pp. 71-72. Autrata, R., and Schauer, P. (1998). Single crystal scintillation detectors for LVSEM, in Proceedings of the Fourteenth International Congress on Electron Microscopy, Vol. 1, edited by H. A. Calderon Benavides and M. J. Yacaman. Bristol, UK: Institute of Physics, pp. 437-438. Barth, J. E., and Kruit, P. (1996). Addition of different contributions to the charged particle probe size. Optik 101, 101-109. Bartog, I., van Hove, M. A., and Altman, M. S. (1996). Cu (111) electron band structure and channeling by VLEED. Surface Sci. 352-354, 660-664. Bauer, E. (1962). Low energy electron reflection microscopy, in Proceedings of the Fifth International Congress on Electron Microscopy, Vol. I, edited by S. S. Bresse, Jr. New York: Academic Press, pp. D 11-12. Bauer, E. (1994). Low energy electron microscopy. Rep. Progr. Phys. 57, 895-938. Bauer, E., and Telieps, W. (1988). Emission and low-energy reflection electron microscopy, in Surface and Interface Characterization by Electron Optical Methods, edited by A. Howie and U. Valdre, New York: Plenum Press, pp. 195-233. Bauer, H. D. (1979). Messungen zur Energieverteilung von Rtickstreu-elektronen an polykristallinen Festk6rpern. Exp. Techn. Phys. 27, 331-344. Bauer, H. E., and Seiler, H. (1984). Determination of the non-charging electron beam energies of electrically floating metal samples, in Scanning Electron Microscopy, Vol. III, edited by O. Johari. Chicago: SEM, pp. 1081-1088. Beck, S., Plies, E., and Schiebel, B. (1995). Low-voltage probe forming columns for electrons. Nucl. Instrum. Methods Phys. Res. A 363, 31-42. Berry, V. K. (1988). Characterization of polymer blends by low voltage scanning electron microscopy. Scanning 10, 19-27. Bindi, R., Lanteri, H., and Rostaing, P. (1980). A new approach and resolution method of the Boltzman equation applied to secondary electron emission by reflection from polycrystalline aluminum. J. Phys. D." Appl. Phys. 13, 267-280. Bleloch, A. L., Howie, A., and Milne, R. H. (1989). High resolution secondary electron imaging and spectroscopy. Ultramicroscopy 31, 99-110. Bode, M., and Reimer, L. (1985). Detector strategy for a single-polepiece lens. Scanning 7, 125-133. B6ngeler, R., Golla, U., K/issens, M., Reimer, L., Schindler, B., Senkel, R., and Spranck, M. (1993). Electron-specimen interactions in low-voltage scanning electron microscopy. Scanning 15, 1-18. Born, M., and Wolf, E. (1975). Principles of Optics. Oxford: Pergamon Press. Brown, A. C., and Swift, J. A. (1974). Low voltage scanning electron microscopy of keratin fibre surfaces, in Scanning Electron Microscopy, edited by O. Johari. Chicago: SEM, pp. 68-74. Bruining, H. (1954). Physics and Application of Secondary Electron Emission. Oxford: Pergamon Press. Brunner, M., and Schmid, R. (1987). Characteristics of an electric/magnetic quadrupole detector for low voltage scanning electron microscopy. Scanning Microsc. 1, 1501-1506. Burns, J. (1960). Angular distribution of secondary electrons from (100) faces of Cu and Ni. Phys. Rev. 119, 102-114.
434
MOLLEROVA AND FRANK
Buseck, P., Cowley, J., and Eyring, L. (1988). High-Resolution Transmission Electron Microscopy and Associated Techniques. London: Oxford University Press. Cailler, M., Ganachaud, J. P., and Bourdin, J. P. (1981). The mean free path of an electron in copper between two inelastic collisions. Thin Solid Films 75, 181-189. Cazaux, J. (1986). Some considerations on the electric field induced in insulators by electron bombardment. J. Appl. Phys. 59, 1418-1430. Cazaux, J. (1996a). Electron probe microanalysis in insulating materials: quantification problems and some possible solutions. X-ray Spectrom. 25, 265-280. Cazaux, J. (1996b). The electric image effects at dielectric surfaces. IEEE Trans. Diel. Electr. Insul. 3, 75-79. Cazaux, J. (1999). Some considerations on the secondary electron emission, 3, from eirradiated insulators. J. Appl. Phys. 85, 1137-1147. Cazaux, J., and Le Gressus, C. (1991). Phenomena relating to charge in insulators: macroscopic effects and microscopic causes. Scanning Microsc. 5, 17-27. Cazaux, J., and Lehuede, P. (1992). Some physical descriptions of the charging effects of insulators under incident particle bombardment. J. El. Spectrosc. Rel. Phenom. 59, 49-71. Cazaux, J., Kim, K. H., Jbara, O., and Salace, G. (1991). Charging effects of MgO under electron bombardment and nonohmic behaviour of the induced specimen current. J. Appl. Phys. 70, 960-965. Chung, M. S., and Everhart, T. E. (1974). Simple calculation of energy distribution of lowenergy secondary electrons emitted from metals under electron bombardment. J. Appl. Phys. 45, 707-709. Czyzewski, Z., and Joy, D. C. (1989). Fast Monte Carlo method for simulating electron scattering in solids. J. Microscopy 156, 285-291. Czyzewski, Z., MacCallum, D. O., Romig, A., and Joy, D. C. (1990). Calculations of Mott scattering cross-section. J. Appl. Phys. 68, 3066-3072. Dahl, D. A. (1995). SIMION 3D Version 6.0, in Proceedings of the Forty-Third ASMS Conference on Mass Spectrometry and Allied Topic. Santa Fe, NM: American Society for Mass Spectrometry, p. 717. Dekker, A. J. (1958). Secondary electron emission. Solid State Phys. 6, 251-315. Delong, A., and Draho~, V. (1971). Low-energy electron diffraction in an emission electron microscope. Nature Phys. Sci. 230, 196-197. Dietrich, W., and Seiler, H. (1960). Energieverteilung von Elektronen, die durch Ionen und Elektronen in Durchstrahlung an dfinnen Folien ausgel6st werden. Z. Angew. Physik 157, 576-585. Ding, Z.-J. (1990). Fundamental studies on the interactions of kV electrons with solids for application to electron spectroscopies. Ph.D. Thesis, Osaka University, Japan. Ding, Z.-J., and Shimizu, R. (1996). A Monte Carlo modeling of electron interaction with solids including cascade secondary electron production. Scanning 18, 92-113. Drescher, H., Reimer, L., and Seidel, H. (1970). Rfickstreukoeffizient und Sekund~irelektronenAusbeute von 10-100 keV Elektronen und Beziehungen zur Raster-Elektronenmikroskopie. Z. Angew. Physik 29, 331-336. Drucker, J., Scheinfein, M. R., Liu, J., and Weiss, J. K. (1993). Electron coincidence spectroscopy studies of secondary and Auger-electron generation mechanisms. J. Appl. Phys. 74, 7329-7339. Egerton, R. F. (1986). Electron Energy-Loss Spectroscopy in the Electron Microscope. New York: Plenum Press. E1-Gomati, M. M., Barkshire, I., Greenwood, J., Kenny, P., Roberts, R., and Prutton, M. (1992). Compositional imaging in scanning Auger microscopy, in: Microscopy." The Key Research Tool, edited by C. Lyman. Chicago: Electron Microscopy Society of America, pp. 29-38.
SCANNING LEEM
435
EI-Gomati, M. M., Romanovsk~,, V., Frank, L., and Mtillerovfi, I. (2002). A very low energy electron column for surface studies, in Proceedings of the Fifteenth International Congress on Electron Microscopy, Vol. 3, edited by R. Cross, J. Engelbrecht, T. Sewell, M. Witcomb, and P. Richards. Onderstepoort: Microscopy Society of Southern Africa, pp. 323-324. E1-Gomati, M. M., Wells, T. C. R., Mtillerovfi, I., Frank, L., and Jayakody, H. (2003). Why is it that diferently doped regions in semiconductors are visible in low voltage SEM? IEEE Trans. Electron Devices, submitted. Everhart, T. E., and Chung, M. S. (1972). Idealized spatial emission distribution of secondary electrons. J. Appl. Phys. 43, 3708-3711. Everhart, T. E., and Thornley, R. F. M. (1960). Wideband detector for micro-micro-ampere low electron currents. J. Sci. Instrum. 37, 246-248. Everhart, T. E., Saeki, N., Shimizu, R., and Koshikawa, T. (1976). Measurement of structure in the energy distribution of slow secondary electrons from aluminum. J. Appl. Phys. 47, 2941-2945. Ezumi, M., Otaka, T., Mori, H., Todokoro, H., and Ose, Y. (1996). Development of critical dimension measurement scanning electron microscope for ULSI (S-8000 series). Hitachi Instrument News Electron Microscopy Edition 30, 15-21. Feldman, L. C., and Mayer, J. W. (1986). Fundamentals of Surface and Thin Film Analysis. New York: Elsevier. Fitting, H.-J., Schreiber, E., Kuhr, J.-Ch., and von Czarnowski, A. (2001). Attenuation and escape depths of low-energy electron emission. J. El. Spectrosc. Rel. Phenom. 119, 35-47. Fourie, J. T. (1976). Contamination phenomena in cryopumped TEM and ultrahigh vacuum field-emission STEM systems, in Scanning Electron Microscopy, Vol. I, edited by O. Johari. Chicago: SEM, pp. 53-60. Fourie, J. T. (1979). A theory of surface-originating contamination and a method for its elimination, in Scanning Electron Microscopy, Vol. II, edited by O. Johari. Chicago: SEM, pp. 87-102. Fourie, J. T. (1981). Electric effects in contamination and electron beam etching, in Scanning Electron Microscopy, Vol. I., edited by O. Johari. Chicago: SEM, pp. 127-134. Frank, L. (1992a). Towards electron beam tomography, in Proceedings of the Tenth European Congress on Electron Microscopy, Vol. 1, edited by A. Rios, J.M. Arias, L. Megias-Megias, and A. Lopez-Galindo. Granada: Univ. de Granada, pp. 141-142. Frank, L. (1992b). Experimental study of electron backscattering at interfaces. Surface Sci. 269/270, 763-771. Frank, L. (1996a). Real image resolution of SEM and low-energy SEM and its optimization. Ultramicroscopy 62, 261-269. Frank, L. (1996b). Width of the SEM and LESEM response function as a tool for the image resolution assessment, in Proceedings of the Ninth Conference on Electron Microscopy of Solids, edited by A. Czyrska-Filemonowicz. Krak6w: State Committee for Scientific Research, pp. 109-112. Frank, L. (2002). Advances in scanning electron microscopy, in Advances in Imaging and Electron Physics, Vol. 123, edited by P. W. Hawkes. San Diego: Academic Press, pp. 327-373. Frank, L., and Mtillerovfi, I. (1994). Zero-charging electron microscopy in a cathode lens equipped SEM, in Proceedings of the Thirteenth International Congress on Electron Microscopy, Vol. 1, edited by B. Jouffrey and C. Colliex. Les Ulis, France: Les 6ditions de Physique, pp. 139-140. Frank, L., and Mtillerovfi, I. (1999). Strategies for low- and very-low-energy SEM. J. El. Microsc. 48, 205-219. Frank, L., Mtillerovfi, I., and E1-Gomati, M. M. (2000a). A novel in-lens detector for electrostatic scanning LEEM column. Ultramicroscopy 81, 99-110.
436
MOLLEROV~i AND FRANK
Frank, L., Mfillerovfi, I., and E1-Gomati, M. M. (2002). SEM visualization of doping in semiconductors, in Proceedings of the Fifteenth International Congress on Electron Microscopy, Vol. 1, edited by R. Cross, J. Engelbrecht, M. Witcomb, and P. Richards. Onderstepoort: Microscopy Society of Southern Africa, pp. 39-40. Frank, L., Mfillerovfi, I., Faulian, K., and Bauer, E. (1999). The scanning low-energy electron microscope: first attainment of diffraction contrast in the scanning electron microscope. Scanning 21, 1-13. Frank, L., Stekb,, R., Zadra~il, M., E1-Gomati, M. M., and Mfillerovfi, I. (2000b). Electron backscattering from real and in situ treated surfaces. Mikrochim. Acta 132, 179-188. Frank, L., Zadra~il, M., and Mtillerovfi, I. (2001). Scanning electron microscopy of nonconductive specimens at critical energies in a cathode lens system. Scanning 23, 36-50. Frosien, J., and Plies, E. (1987). High performance electron optical column for testing ICs with submicrometer design rules. Microelectronic Engineering 7, 163-172. Frosien, J., Plies, E., and Anger, K. (1989). Compound magnetic and electrostatic lenses for low voltage applications. J. Vac. Sci. Technol. B 7, 1874-1877. Gergely, G. (1986). Elastic peak electron spectroscopy. Scanning 8, 203-214. Gergely, G., Menyhfird, M., and Sulyok, A. (1986). Some new possibilities in non-destructive depth profiling using secondary emission spectroscopy: REELS and EPES. Vacuum 36, 471-475. Glaser, W. (1952). Grundlagen der Elektronenoptik. Wien: Springer-Verlag. Gries, W. H., and Werner, W. (1990). Take-off angle and film thickness dependences of the attenuation length of x-ray photoelectrons by a trajectory reversal method. Surf Interf. Anal. 16, 149-153. Gryzinski, M. (1965). Classical theory of atomic collisions. I. Theory of inelastic collisions. Phys. Rev. A 138, 336-358. Hachenberg, O., and Brauer, W. (1959). Secondary electron emission from solids, in Advances in Electronics and Electron Physics, Vol. II, edited by L. Marton. San Diego: Academic Press, pp. 413-499. Hasselbach, F., and Krauss, H.-R. (1988). Backscattered electrons and their influence on contrast in the scanning electron microscope. Scanning Microsc. 2, 1947-1956. Hasselbach, F., and Rieke, U. (1982). Spatial distribution of secondaries released by backscattered electrons in silicon and gold for 20-70 keV primary energy, in Proceedings of the Tenth International Congress on Electron Microscopy, Vol. 1, edited by the Congressional Organization Committee. Hamburg: Deutsche Ges. EM, pp. 253-254. Hawkes, P. W. (1997). Aberrations, in Handbook of Charged Particle Optics, edited by J. Orloff. New York: CRC Press, pp. 223-274. Hawkes, P. W., and Kasper, E. (1996a). Principles of Electron Optics Vol. 2, Applied Geometrical Optics. San Diego: Academic Press. Hawkes, P. W., and Kasper, E. (1996b). Principles of Electron Optics Vol. 3, Wave Optics. San Diego: Academic Press. Hejna, J. (1994). Backscattered electron imaging in low-voltage SEM, in Proceedings of the Thirteenth International Congress on Electron Microscopy, Vol. 1, edited by B. Jouffrey and C. Colliex. Les Ulis, France: Les 6ditions de Physique, pp. 75-76. Hejna, J. (1998). Optimization of an immersion lens design in the BSE detector for the low voltage SEM, in Recent Trends in Charged Particle Optics and Surface Physics Instrumentation, Sixth Seminar, edited by I. Mfillerovfi and L. Frank. Brno: Czechoslovak Society for Electron Microscopy, pp. 30-31. Ho, Y. C., Tan, Z. Y., Wang, X. L., and Chen, J. G. (1991). A theory and Monte Carlo calculation on low-energy electron scattering in solids. Scanning Microsc. 4, 945-951.
SCANNING LEEM
437
Homma, Y., Suzuki, M., and Tomita, M. (1993). Atomic configuration dependent secondary electron emission from reconstructed silicon surfaces. Appl. Phys. Lett. 62, 3276-3278. Huta~, O., Oral, M., Mtillerov/t, I., and Frank, L. (2000). Dimension measurement in a cathode lens equipped low-energy SEM, in Proceedings of the Twelfth European Congress on Electron Microscopy, Vol. 3, edited by L. Frank and F. Ciampor. Brno: Czechoslovak Society for Electron Microscopy, pp. 199-200. Ichimura, S. (1980). Basic study of scanning Auger electron microscopy for surface analysis. Ph.D. Thesis, Osaka University, Japan. Ichinokawa, T., Ishikawa, Y., Kemmochi, M., Ikeda, N., Hosokawa, Y., and Kirschner, J. (1986). Low-energy scanning electron microscopy combined with low-energy electron diffraction. Surface Sci. 176, 397-414. Ichinokawa, T., Ishikawa, Y., Kemmochi, M., Ikeda, N., Hosokawa, Y., and Kirschner, J. (1987). Scanning low-energy electron microscopy. Scanning Microsc. Suppl. 1, 93-97. Ishikawa, Y., Ikeda, N., Kemmochi, M., and Ichinokawa, T. (1985). UHV-SEM observations of cleaning process and step formation on silicon (111) surfaces by annealing. Surface Sci. 159, 256-264. Jacka, M., Kirk, M., E1-Gomati, M. M., and Prutton, M. (1999). A fast, parallel acquisition, electron energy analyzer: The hyperbolic field analyzer. Rev. Sci. Instrum. 70, 2282-2287. Jaklevic, R. C., and Davis, L. C. (1982). Band signatures in the low-energy-electron reflectance spectra for fcc metals. Phys. Rev. B 26, 5391-5397. Joy, D. C. (1984). Beam interactions, contrast and resolution in the SEM. J. Microsc. 136, 241-258. Joy, D. C. (1987). A model for calculating secondary and backscattered electron yields. J. Microsc. 147, 51-64. Joy, D. C. (1989). Control of charging in low-voltage SEM. Scanning 11, 1-4. Joy, D. C. (1995). Monte Carlo Modeling for Electron Microscopy and Microanalysis. Oxford Series in Optical and Imaging Sciences. London: Oxford University Press. Joy, D. C. (2001). A database of electron-solid interactions, Rev. 01-01. http://web.utk.edu/ srcutk/htm/interact.htm. Joy, D. C., and Joy, C. S. (1996). Low voltage scanning electron microscopy. Micron 27, 247-263. Joy, D. C., and Luo, S. (1989). An empirical stopping power relationship for low-energy electrons. Scanning 11, 176-180. Kanaya, K., and Kawakatsu, H. (1972). Secondary electron emission due to primary and backscattered electrons. J. Phys. D: Appl. Phys. 5, 1727-1742. Kanter, H. (1961). Contribution of backscattered electrons to secondary electron formation. Phys. Rev. 121, 681-684. Kato, M., and Tsuno, K. (1990). Numerical analysis of trajectories and aberrations of a Wien filter including the effect of fringing fields. Nucl. Instrum. Meth. Phys. Res. A298, 296-320. Kazumori, H. (2002). Development of JSM-7400F: new secondary electron detection systems permit observation of non-conductive materials. JEOL News 37E(1), 44-47. Khursheed, A. (2002). Aberration characteristics of immersion lenses for LVSEM. Ultramicroscopy 93, 331-338. Kirschner, J. (1984). On the role of the electron spin in scanning electron microscopy, in Scanning Electron Microscopy, Vol. III. edited by O. Johari. Chicago: SEM, pp. 1179-1185. Knell, G., and Plies, E. (1998). Determination of the collection efficiency for combined magnetic-electrostatic SEM objective lenses. Optik 108, 37-42. Kohl, H., Rose, H., and Schnabl, H. (1981). Dose-rate effect at low temperatures in FBEM and STEM due to object heating. Optik 58, 11-24.
438
MfSLLEROV.~ AND FRANK
Kolafik, R., and Lenc, M. (1997). An expression for the resolving power of a simple optical system. Optik 106, 135-139. Kollath, R. (1956). Sekundfirelektronen-Emission fester K6rper bei Bestrahlung mit Elektronen, in Handbuch der Physik, Vol. 21. Berlin: Springer-Verlag, pp. 232-303. Kruit, P., and Lenc, M. (1992). Optical properties of the magnetic monopole field applied to electron microscopy and spectroscopy. J. Appl. Phys. 72, 4505-4513. Kuhr, J.-Ch., and Fitting, H.-J. (1998). Monte-Carlo simulation of low-voltage scanning electron microscopy--LVSEM, in Proceedings of the Fourteenth International Congress on Electron Microscopy, Vol. 1, edited by H.A. Calderon Benavides and M.J. Yacaman. Bristol, UK: Institute of Physics, pp. 451-452. Kuhr, J.-Ch., and Fitting, H.-J. (1999). Monte Carlo simulation of electron emission from solids. J. El. Spectrosc. Rel. Phenom. 105, 257-273. Kulenkampff, H., and Spyra, W. (1954). Energieverteilung rtickdiffundierter Elektronen. Z. Phys. 137, 416-425. Le Gressus, C., Valin, F., Gautier, M., Duraud, J. P., Cazaux, J., and Okuzumi, H. (1990). Charging phenomena on insulating materials: mechanisms and applications. Scanning 12, 203-210. Lenc, M. (1995). Immersion objective lenses for very low energy electron microscopy, in Proceedings of the Multinational Congress on Electron Microscopy, edited by F. Ciampor. Bratislava: Slovak Academic Press, pp. 103-104. Lenc, M., and Mtillerovfi, I. (1992a). Electron optical properties of a cathode lens. Ultramicroscopy 41, 411-417. Lenc, M., and Mtillerovfi, I. (1992b). Optical properties and axial aberration coefficients of the cathode lens in combination with a focusing lens. Ultramicroscopy 45, 159-162. Lencovfi, B. (1997). Electrostatic lenses. Handbook of Charged Particle Optics, edited by J. Orloff. New York: CRC Press, pp. 177-221. Lencovfi, B., and Wisselink, G. (1990). Program package for the computation of lenses and deflectors. Nucl. Instrum. Meth. A298, 56-66. Libinson, A. G. (1999). Tilt dependence of secondary electron emission at low excitation energy. Scanning 21, 23-26. Liebel, H., and ~Senftinger, B. (1991). Low-energy electron microscope of novel design. Ultramicroscopy 36, 91-98. Llacer, J., and Garwin, E. L. (1969). Electron-phonon interaction in alkali halides~I. The transport of secondary electrons with energies between 0.25 and 7.5 eV. J. Appl. Phys. 40, 2766-2775. Mankos, M., and Adler, D. (2002). Electron-electron interactions in cathode objective lenses. Ultramicroscopy 93, 347-354. Martin, J. P., Weimer, E., Frosien, J., and Lanio S. (1994). Ultra-high resolution SEM--A new approach. Microscopy and Analysis (USA), March, 19. McKernan, S. (1998). A comparison of detectors for low voltage contrast in the SEM, in Proceedings of the Fourteenth International Congress on Electron Microscopy, Vol. 1, edited by H. A. Calderon Benavides and M. J. Yacaman. Bristol, UK: Institute of Physics, pp. 481-482. Meisburger, W. D., Brodie, A. D., and Desai, A. A. (1992). Low-voltage electron-optical system for the high-speed inspection of integrated circuits. J. Vae. Sci. Technol. B 10, 2804-2808. Miyoshi, M., Yamazaki, Y., Nagai, T., and Nagahama, I. (1999). Development of a projection imaging electron microscope with electrostatic lenses. J. Vac. Sci. Technol. B 17, 2799-2802. Morin, P., Pitaval, M., and Vicario, E. (1976). Direct observation of insulators with a scanning electron microscope. J. Phys. E: Sci. Instrum. 9, 1017-1020.
SCANNING LEEM
439
Mott, N. F., and Massey, H. S. W. (1965). The Theory of Atomic Collisions. London: Oxford University Press. Mfillerovfi, I. (1996). Contrast mechanisms in low voltage SEM, in Proceedings of the Ninth Conference on Electron Microscopy of Solids, edited by A. Czyrska-Filemonowicz. Krak6w: State Committee for Scientific Research, pp. 93-96. Mfillerov~, I. (2001). Imaging of specimens at optimized low and very low energies in scanning electron microscopes. Scanning 23, 379-394. Mfillerovfi, I., and Frank, L. (1993). Very low energy microscopy in commercial SEMs. Scanning 15, 193-201. Mfillerov~, I., and Frank, L. (1994). Use of cathode lens in scanning electron microscope for low voltage applications. Mikrochim. Acta 114/115, 389-396. Mfillerovfi, I., and Frank, L. (2002). Practical resolution limit in the scanning lowenergy electron microscope, in Proceedings of the Fifteenth International Congress on Electron Microscopy, Vol. 3, edited by R. Cross, J. Engelbrecht, T. Sewell, M. Witcomb, and P. Richards. Onderstepoort: Microscopy Society of Southern Africa, pp. 99-100. Mfillerovfi, I., and Frank, L. (2003). Contrast at very low energies of the gold/carbon specimen for resolution testing. Scanning, submitted. Mfillerovfi, I., and Lenc, M. (1992a). Some approaches to low-voltage scanning electron microscopy. Ultramicroscopy 41, 399-410. Mfillerov~, I., and Lenc, M. (1992b). The scanning very-low-energy electron microscope (SVLEEM). Mikrochim. Acta (Suppl.) 12, 173-177. Mfillerov~t, I., E1-Gomati, M. M., and Frank, L. (2002). Imaging of the boron doping in silicon using low-energy SEM. Ultramicroscopy 93, 223-243. Mfillerovfi, I., Frank, L., and HutaL O. (2001). Visualization of the energy band contrast in SEM through low-energy electron reflectance. Scanning 23, 115. Mfillerovfi, I., Lenc, M., and Florifin, M. (1989). Collection of backscattered electrons with a single polepiece lens and a multiple detector. Scanning Microsc. 3, 419-428. Mfillerov~, I., Zadra~il, M., and Frank, L. (1997). Low-energy SEM imaging of bevelled multilayers. J. Comput. Assist. Microsc. 9, 121-122. Mulvey, T. (1984). Magnetic electron lenses II, in Electron Optical Systems for Microscopy, Microanalysis and Microlithography, edited by J. J. Hren, F. A. Lenz, E. Munro, and P. B. Sewell. Chicago: SEM, pp. 15-27. Nagatani, T., Saito, S., Sato, M., and Yamada, M. (1987). Development of an ultrahigh resolution SEM by means of a field emission source and in-lens system. Scanning Microsc. 1, 901-909. Nieminen, R. M. (1988). Stopping power for low-energy electrons. Scanning Microsc. 2, 1917-1926. Ono, S., and Kanaya, K. (1979). The energy dependence of secondary emission based on the range-energy retardation power formula. J. Phys. D: Appl. Phys. 12, 619-632. Paden, R. S., and Nixon, W. C. (1968). Retarding field scanning electron microscopy. J. Phys. E: Sci. Instrum. 1, 1073-1080. Pawley, J. B. (1984). Low voltage scanning electron microscopy. J. Microsc. 136, 45-68. Pejchl, D., Mfillerov~, I., and Frank, L. (1993). Unconventional imaging of surface relief. Czech. J. Phys. 43, 983-992. Pejchl, D., Mfillerov~, I., Frank, L., and Kolafik, V. (1994). Separator of primary and signal electrons for very-low-energy SEM. Czech. J. Phys. 44, 269-276. Penn, D. R. (1987). Electron mean free path calculations using a model dielectric function. Phys. Rev. B 35, 482-486.
440
MULLEROVA AND FRANK
Pfefferkorn, G. E., Gruter, H., and Pfautsch, M. (1972). Observations on the prevention of specimen charging, in Scanning Electron Microscopy, Vol. I, edited by O. Johari. Chicago: SEM, pp. 147-152. Plies, E., Degel, B., Hayn, A., Knell, G., and Schiebel, B. (1998). Experimental results using a "low-voltage booster" in a conventional SEM, in Proceedings of the Fifth International Conference on Charged Particle Optics, edited by P. Kruit and P. W. van Amersfoort. Amsterdam: Elsevier, pp. 126-130. Powell, C. J. (1974). Attenuation lengths of low-energy electrons in solids. Surface Sci. 44, 29-46. Powell, C. J. (1984). Inelastic mean free paths and attenuation lengths of low-energy electrons in solids, in Scanning Electron Microscopy, Vol. IV, edited by O. Johari. Chicago: SEM, pp. 1649-1664. Powell, C. J. (1985). Calculations of electron inelastic mean free paths from experimental optical data. Surf Interf. Anal. 7, 263-274. Powell, C. J. (1987). The energy dependence of electron inelastic mean free path. Surf Interf. Anal. 10, 349-354. Preikszas, D., and Rose, H. (1995). Procedures for minimizing the aberrations of electromagnetic compound lenses. Optik 100, 179-187. Price, C. W., and McCarthy, P. L. (1988). Low voltage scanning electron microscopy of lowdensity materials. Scanning 10, 29-36. Rao-Sahib, T. S., and Wittry, D. B. (1974). X-ray continuum from thick element targets for 1050 keV electrons. J. Appl. Phys. 45, 5060-5068. Recknagel, A. (1941). Theorie des elektrischen Elektronenmikroskops fiir Selbststrahler. Z. Phys. 117, 689-708. Reimer, L. (1971). Rauschen der Sekundfirelektronenemission. Beitr(ige Elektr. Direktabb. Oberfldichen (BEDO) 412, 299-304. Reimer, L. (1995). In Energy-Filtering Transmission Electron Microscopy, edited by L. Reimer. Berlin: Springer-Verlag, pp. 7-9. Reimer, L. (1996). MOCASIM--Ein Monte Carlo Programm ffir Forschung und Lehre. Beitr. Elektr. Mikr. Direktabb. Oberfl. (BEDO) 29, 1-10. Reimer, L. (1998). Scanning Electron Microscopy. Berlin: Springer-Verlag. Reimer, L., and Kfissens, M. (1994). Application of a two-detector system for secondary and backscattered electrons in LVSEM, in Proceedings of the Thirteenth International Congress on Electron Microscopy, Vol. 1, edited by B. Jouffrey and C. Colliex. Les Ulis, France: Les 6ditions de Physique, pp. 73-74. Reimer, L., and Wfichter, M. (1978). Contribution to the contamination problem in TEM. Ultramicroscopy 3, 169-174. Reimer, L., B6ngeler, R., K~issens, M., Liebscherr, F. F., and Senkel, R. (1991). Calculation of energy spectra from layered structures for backscattered electron spectrometry and relations to Rutherford backscattering spectrometry by ions. Scanning 13, 381-391. Reimer, L., Golla, U., B6ngeler, R., Kfissens, M., Schindler, B., and Senkel, R. (1992). Charging of bulk specimens, insulating layers and free supporting films in scanning electron microscopy. Optik 92, 14-22. Reimer, L., and L6dding, B. (1984). Calculation and tabulation of Mott cross-sections for large-angle scattering. Scanning 6, 128-151. Reimer, L., and Tollkamp, C. (1980). Measuring the backscattering coefficient and secondary electron yield inside a SEM. Scanning 8, 35-39. Rose, H. (1987). The retarding Wien filter as a high-performance imaging filter. Optik 77, 26-34. Rose, H., and Preikszas, D. (1992). Outline of a versatile corrected LEEM. Optik 92, 31-44.
SCANNING LEEM
441
Rose, H., and Spehr, R. (1980). On the theory of the Boersch effect. Optik 57, 339-364. Salehi, M., and Flinn, E. A. (1981). Dependence of secondary electron emission from amorphous materials on primary angle of incidence. J. Appl. Phys. 52, 994-996. Sato, M., Todokoro, H., and Kageyama, K. (1993). A snorkel type objective lens with E x B field for detecting secondary electrons. SPIE 2014, 17-23. Schfifer, J., and H61zl, J. (1972). A contribution to the dependence of secondary electron emission from the work function and Fermi energy. Thin Solid Films 18, 81-86. Schauer, P., and Autrata, R. (1998). Computer optimized design of BSE scintillation detector for SEM, in Proceedings of the Eleventh European Congress on Electron Microscopy, Vol. I, edited by Committee of European Societies for Microscopy. Brussels: CESM, pp. 369-370. Schmid, R., and Brunner, M. (1986). Design and application of a quadrupole detector for lowvoltage scanning electron microscopy. Scanning 8, 294-299. Schmid, R., Gaukler, K.H., and Seiler, H. (1983). Measurement of elastically reflected electrons (E _<2.5 keV) for imaging of surfaces in a simple ultra high vacuum scanning electron microscope, in Scanning Electron Microscopy, Vol. II, edited by O. Johari. Chicago: AMF O'Hare, pp. 501-509. Schreiber, E., and Fitting, H.-J. (2002). Monte Carlo simulation of secondary electron emission from the insulator SiO2. J. El. Spectrosc. Rel. Phenom. 124, 25-37. Seah, M. P., and Dench, W. A. (1979). Quantitative electron spectroscopy of surfaces: a standard database for electron inelastic mean free paths in solids. Surf Interf. Anal. 1, 1-11. Sealy, C. P., Castell, M. R., and Wilshaw, P. R. (2000). Mechanism for secondary electron dopant contrast in the SEM. J. El. Microsc. 49, 311-321. Seiler, H. (1967). Some problems of secondary electron emission. Z. Angew. Physik 22, 249-263. Seiler, H. (1983). Secondary electron emission in the scanning electron microscope. J. Appl. Phys. 54, R l-R18. Seiler, H., and Kuhnle, G. (1970). Anisotropy of the secondary electron yield as a function of the energy of the primary electrons from 5 to 20 keV. Z. Angew. Physik 29, 254-260. Shaffner, T. J., and Van Veld, R. D. (1971). "Charging" effects in the scanning electron microscope. J. Phys. E: Sci. Instrum. 4, 633-637. Shao, Z. (1989). Extraction of secondary electrons in a newly proposed immersion lens. Rev. Sci. Instrum. 60, 693-699. Spehr, R. (1985). Broadening of charged particle microprobes by stochastic Coulomb interactions. Optik 70, 109-114. Strocov, V. N., and Starnberg, H. I. (1995). Absolute band-structure determination by target current spectroscopy: Application to Cu(100). Phys. Rev. B 52, 8759-8765. Strocov, V. N., Starnberg, H. I., Nilsson, P. O., and Holleboom, L. J. (1996). Determining unoccupied bands of layered materials by VLEED: implications for photoemission band mapping. J. Phys.. Condens. Matter 8, 7549-7559. Takashima, S. (1994). New electron optical technologies in low voltage scanning electron microscope. JEOL News 31E(1), 33-35. Tanuma, S., Powell, C. J., and Penn, D. R. (1991a). Calculations of electron inelastic mean free paths II. Data for 27 elements over the 50-2000 eV range. Surf Interf. Anal. 17, 911-926. Tanuma, S., Powell, C. J., and Penn, D. R. (1991b). Calculations of electron inelastic mean free paths III. Data for 15 inorganic compounds over the 50-2000 eV range. Surf Interf. Anal. 17, 927-939. Telieps, W. (1987). Surface imaging with LEEM. Appl. Phys. A 44, 55-61. Telieps, W., and Bauer, E. (1985). An analytical reflection and emission UHV surface electron microscope. Ultramieroscopy 17, 57-66. Thomas, S., and Pattinson, E. B. (1970). Range of electrons and contribution of back-scattered electrons in secondary production in aluminum. J. Phys. D: Appl. Phys. 3, 349-357.
442
M[ILLEROV,~i AND FRANK
Tromp, R. M. (2000). Low-energy electron microscopy. IBM J. Res. Develop. 44, 503-516. Tromp, R. M., and Reuter, M. C. (1993). Imaging with a low-energy electron microscope. Ultramicroscopy 50, 171-178. Tromp, R. M., Denier van der Gon, A. W., LeGoues, F. K., and Reuter, M. C. (1993). Observation of buried interfaces with low-energy electron microscopy. Phys. Rev. Lett. 71, 3299-3302. Tsai, F. C., and Crewe, A. V. (1998). A gapless magnetic objective lens for low voltage SEM. Optik 109, 5-11. Tung, C. J., Ashley, J. C., and Ritchie, R. H. (1979). Electron inelastic mean free paths and energy losses in solids, II. Electron gas statistical model. Surface Sci. 81, 427-439. Veneklasen, L. H. (1992). The continuing development of low-energy electron microscopy for characterizing surfaces. Rev. Sci. Instrum. 63, 5513-5532. Welter, L. M., and McKee, A. N. (1972). Observations on uncoated, nonconducting or thermally sensitive specimens using a fast scanning field emission source SEM, in Scanning Electron Microscopy, Vol. I, edited by O. Johari. Chicago: SEM, pp. 161-166. Werner, W. S. M. (1992). The role of the attenuation parameter in electron spectroscopy. J. El. Spectrosc. Rel. Phenom. 59, 275-291. Werner, W. S. M. (1996). Transport equation approach to electron microbeam analysis: fundamentals and applications. Mikrochim. Acta (Suppl.) 13, 13-38. Woodruff, D. P., and Delchar, T. A. (1986). Modern Techniques of Surface Science. Cambridge: Cambridge University Press. Ximen, J., Lin, P. S. D., Pawley, J. B., and Schippert, M. (1993). Electron optical design of a high-resolution low-voltage scanning electron microscope with field emission gun. Rev. Sci. Instrum. 64, 2905-2910. Yau, Y. W., Pease, R. F. W., Iranmanesh, A. A., and Polasko, K. J. (1981). Generation and applications of finely focused beams of low-energy electrons. J. Vac. Sci. Technol. 19, 1048-1052. Zach, J. (1989). Design of a high-resolution low-voltage scanning electron microscope. Optik 83, 30-40. Zach, J., and Haider, M. (1992). A high-resolution low voltage scanning electron microscope, in Proceedings of the Tenth European Congress on Electron Microscopy, Vol. 1, edited by A. Rios, J.M. Arias, L. Megias-Megias, and A. Lopez-Galindo. Granada: Univ. de Granada, pp. 49-53. Zach, J., and Rose, H. (1986). Efficient detection of secondary electrons in low-voltage scanning electron microscopy. Scanning 8, 285-293. Zach, J., and Rose, H. (1988). High-resolution low-voltage electron microprobe with large SE detection efficiency, in Proceedings of the Ninth European Congress on Electron Microscopy, Vol. l, edited by P.J. Goodhew and H.G. Dickinson. Bristol, UK: Institute of Physics, pp. 81-82. Zadra~il, M., E1-Gomati, M. M., and Walker, A. (1997). Measurements of very-low-energy secondary and backscattered electron coefficients. J. Comput. Ass. Microsc. 9, 123-124. Zadra~il, M., and E1-Gomati, M. M. (1998a). Measurements of the secondary and backscattered electron coefficients in the very-low-energy range, in Recent Trends in Charged Particle Optics and Surface Physics Instrumentation, Sixth Seminar, edited by I. Miillerov~ and L. Frank. Brno: Czechoslovak Society for Electron Microscopy, p. 82. Zadra~il, M., and E1-Gomati, M. M. (1998b). Measurements of the secondary and backscattered electron coefficients in the energy range 250-5000 eV, in Proceedings of the Fourteenth International Congress on Electron Microscopy, Vol. l, edited by H.A. Calderon Benavides and M.J. Yacaman. Bristol, UK: Institute of Physics, pp. 495-496. Zadra~il, M., and E1-Gomati, M. M. (2002). Unpublished data.
SCANNING LEEM
443
Zoba6ovfi, J., and Frank, L. (2003). Specimen charging and detection of signal from nonconductors in a cathode lens equipped SEM. Scanning, 25, 150-156. Zoba~ovfi, J., Oral, M., Huta~, O., Mtillerovfi, 2., and Frank, L (2003). Corrections of magnification and focusing in a cathode lens equipped SEM. To be submitted. Zworykin, V. A., Hillier, J., and Snyder, R. L. (1942). A scanning electron microscope. A S T M Bull. 117, 15-23.